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  • 2010-2014
  • 1990-1994  (1,629)
  • 1890-1899  (155)
  • 1990  (1,629)
  • 1895  (155)
  • General Chemistry  (1,183)
  • Engineering  (558)
  • Industrial Chemistry and Chemical Engineering
Material
Years
  • 2010-2014
  • 1990-1994  (1,629)
  • 1890-1899  (155)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 1-5 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Practical experience of particle size analysers using the Coulter principle shows that for measurements made over a range of 2% to 60% of the aperture diameter, the aperture responds linearly to particle volume at least for spheres. In this paper it is shown that the response of a focussed aperture is not significantly different from an unfocussed aperture. It is also shown that a simple linear equation of response successfully applied to a COULTER COUNTER® model ZM in a previous paper, can be used to predict the calibration constant of a new wide range instrument, the COULTER® MULTISIZER.
    Additional Material: 2 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 127-130 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new particle size distribution function based on a simple model is presented. Data generated by the normal, log-normal and Rosin-Rammler distribution functions were fitted with this new distribution function and the fitted curves were, for all practical purposes, indistinguishable from all three distributions.The new distribution function can replace all the three functions and thus a means of presenting and comparing the different size distribution patterns in terms of a single mathematical expression is obtained. Additionally, the new distribution function provides the possibility of developing the discussion on the physical meaning of the particle size distribution.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 136-143 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Dispersion of monosized drops downstream a point injection in a grid-generated turbulence is studied. Influence of extra bodyforces is also investigated by use of ferrofluid drops and magnetic field. Datas are obtained through LDV and given for fluid and particles mean and fluctuant velocities. Presence probability repartition for particles downstream the injection is obtained by LDV counting.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A method based on the employment of an electrical sensing zone instrument (Coulter Counter) has recently been proposed for the combined measurement of the increase in particle volume (particle swelling) and granulometric characterization of pharmaceutical tablet disintegrants. The performance of the method, as far as its applicability to limited swelling materials is concerned, has been assessed. Both inert materials (polystyrene latices) and limited swelling disintegrants (maize starch and crospovidone in different granulometric fractions) were examined for total particulate volume in aqueous media. The accuracy and repeatability of measurements of both total particulate volume and particle volume increase were defined. The results obtained indicate that the method may be adapted for measuring the increase in particle volume of so-called limited swelling disintegrants.
    Additional Material: 2 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 121-126 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Various types of floor tile were tested in a controlled and isolated environment to determine quantitatively the wear rate and size characteristics of material generated from floor tile during operations of sanding, cutting, and breaking. Size characteristics were determined for the aerosolized fractions as well as the settled material worn from the tile surface. In addition to the vinyl composition tile, tests were also conducted with floor tile containing various amounts of glass fiber and sodium phosphate fibers. The tests were conducted in a specially designed glove box which allowed complete sampling and fractionization of the generated aerosol. Due to good measurement repeatability, aerosol generation differences from the various flooring types were determinable.A Frick-Taber accelerated wear machine was employed to establish comparative wear rates of the different flooring materials. Test results were repeatable and measured relative wear rates correlate well with published measurements. Results indicate that the presence of up to 13% glass fibers or phosphate fibers in the tile does not improve the tile's wear characteristics or significantly alter the size distribution of the generated material. Although asbestos-containing floor tile was not tested in this study, results from the simulant fiber tile tests may enable prediction of the behavior of vinyl-asbestos tile under the influence of similar wear mechanisms.
    Additional Material: 1 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 169-169 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 11-21 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper describes a novel technique with which a system with changing topology can be modelled whilst maintaining a constant system matrix. This technique employs a new transmission-line switch model which has a constant characteristic impedance, irrespective of its state. The method is explained, compared with the switched-resistance method and demonstrated by two examples. It has been found that the proposed method offers substantial advantages in the formulation of the problems and in the efficiency of computation.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 23-31 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The resonant mode field expansion technique presented in previous papers to analyse one- or two-port microstrip structures of different geometrical shapes is now applied to multiport radial lines. In particular, a radial-line n-way power divider is considered. This device allows, under certain hypotheses, an equiphase and equiamplitude splitting of an input signal. The Z matrix formulation has been derived and utilized to obtain the scattering parameters for the circuit. The numerical results are in good agreement with both experimental and theoretical data presented in the literature. The low number of resonant modes required to obtain satisfactory numerical convergence allows a substantial reduction of the computing time with respect to other more complicated approaches.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 57-71 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The boundary residual method is a powerful technique for solving EM boundary-value problems. This technique produces matrices difficult to solve using many of the standard numerical techniques. This paper discusses lesser-known numerical aspects of this method, and it shows efficient and well-conditioned methods to solve both the homogeneous and non-homogeneous boundary residual problem.
    Additional Material: 5 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 39-56 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The paper describes the application of the TLM numerical method for the analysis of acoustic wave propagation. It presents a general scattering algorithm for modelling homogeneous and inhomogeneous mediums where both the density and compressibility of the propagation space are varied. The method is used to obtain the acoustic radiation patterns of discrete transducer arrays. The effect of the spacing and the number of transducer elements on the radiation pattern are demonstrated by numerical results obtained using a two-dimensional TLM mesh. The results also show the effect of array shading on the radiation pattern. Beam steering by delayed excitation of the transducer elements is also demonstrated here. In addition the paper presents two simple techniques for detecting the direction of wave propagation in the TLM mesh.
    Additional Material: 12 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 73-73 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990) 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 79-90 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The non-linear diffusion mechanism arising in process modelling is analysed via a model problem. Using a scaling of the dopant concentration and an adaptive finite element method, high resolution is obtained in a particularly economical way.
    Additional Material: 5 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 99-110 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A procedure is described for estimating various parameters governing the diffusion of impurities in semiconductors; these parameters are required for a number of explicit numerical models of non-linear diffusion in III-V crystals. The method is based on an analytical solution of the continuum equivalent of a discrete numerical model due to Zahari and Tuck and provides a systematic procedure for analysing experimental data to yield predictions for the coefficient of diffusion of the impurity, the coefficient of self-diffusion of the host material, the bulk equilibrium vacancy concentration and, under conditions of “dissociation” pressure, the surface vacancy concentration. Application of the procedure to two sets of independent experimental data provided reasonably consistent values of the parameters.
    Additional Material: 4 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 111-126 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The paper presents a combined fine-coarse mesh TLM method. This technique reduces the memory storage and the computational time when modelling complex structures. In the combined fine-coarse mesh model, the region of interest is covered with a set of transmission-line fine meshes. The remaining part is covered with regular (or irregular) coarse meshes. The fine-mesh nodes are connected through busbars to the adjacent coarse-mesh nodes. The combined fine-coarse mesh TLM technique is applied to some diffusion problems. Significant savings in computational time and memory storage are obtained without loss of accuracy.
    Additional Material: 20 Ill.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990) 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 3 (1990), S. 137-155 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: When the erosion or growth of a surface that occurs in semiconductor device processing can be considered as everywhere continuous in space and time, the equations of motion of the surface may be specified and determined numerically using a kinetic model of surface evolution. In this review the fundamental concepts of the kinematic model of surface evolution are discussed. Detailed consideration of the theory of characteristics reveals its limitations which are overcome by recent theoretical development based on the Huygens principle of wavefront reconstruction. Correct interpretation of the nature of the basic wavelet, coupled with contemporary ideas of surface and edge propagation, form the essence of a new numerical algorithm. Numerical analysis and consequent numerical procedures derived from the generalized kinematic model are presented. Examples of surface evolution, with particular reference to ion beam induced erosion are given to show the advantages and potential of the method as opposed to existing models and theoretical prediction.When evolution processes are discontinuous and localized, other approaches, particularly those that use numerical modelling, are required. Such approaches are also reviewed here.
    Additional Material: 10 Ill.
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  • 18
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 16-24 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The characteristics of swirling single- and two-phase flows discharging into a sudden pipe expansion were studied in detail by the use of laser-Doppler anemometry. The results are compared with those for the comparable non-swirling case. The central recirculation zone established for a swirl number of 0.56 was found to have an annular shape, which was a result of the subcritical nature of the flow and the area contraction at the end of the test section.The behaviour of the particles in both swirling and non-swirling flow was studied by flow visualization, particle concentration and velocity measurements. Initially, the spreading of the particle jet is about the same for both cases owing to the particle inertia. In the middle of the recirculation bubble the particles start to spread more rapidly under the acting of centrifugal forces established in a swirling flow. This finally results in a high concentration of particles near the wall of the test section and a particle-free region in the core of the vortex. The numerical simulations of the non-swirling flow showed good agreement for both the gas and particle phases in comparison with the experimental results.
    Additional Material: 12 Ill.
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  • 19
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A laser diffraction technique for the on-line measurement of crystal growth rates was developed. The crystal growth experiments were executed in a fluidized bed apparatus with a specially designed measuring chamber. It is typical in crystallization from solutions to deal with non-spherically shaped particles at high suspension densities (3-25 Vol.-%). The results achieved in a first approach with commercially available instruments were not understandable. It was shown that the particle size distributions from experiments at high suspension densities depend on the volume concentration. This effect was examined by experiments with constant particle sizes and different volume concentrations.If the volume concentration is detected and used to correct the results achieved for the particle size distribution, understandable and reproducible results can be obtained.The necessary correlation function for the measurements at high suspension densities is introduced.
    Additional Material: 10 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 30-35 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The current state in shape analysis is distinguished by a number of characterization methods, but the great variety of specific shapes complicates the selection of parameters that are relevant for a particular problem. Therefore, the preferred approach is to characterize single particles "free of presupposition" and to select technologically relevant parameters using cluster and discriminance algorithms.Parameter vectors including elongation, bulkiness, fractal dimension and area-equivalent diameter are calculated on the basis of image analysis. First applications to bacteria and agricultural freestuffs exemplify the concept and illustrate that technologically relevant particle shape analysis permits the classification of single particles and the quantification of property functions.
    Additional Material: 8 Ill.
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  • 21
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 36-43 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Two kinds of standard media for particle size and number-density measurements and calibration are described. Although the main concern is multiple scattering situations, they might also be useful for single and dependent scattering. One medium is made of particles embedded in a solid polymer matrix and the other of particles embedded in a gel. Transmittance measurements at two wavelengths (visible and far-infrared) are used to exemplify the use of these media.
    Additional Material: 7 Ill.
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  • 22
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 44-44 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 23
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 44-44 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 24
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 45-53 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A new laser Doppler method for particle sizing has been developed. In contrast to the standard phase Doppler technique, which uses scattering from plane waves for a measurement, the proposed method employs cylindrical waves of incident light. The main advantage is that signal frequency, instead of the signal phase, becomes a function of particle diameter and a standard frequency measuring device may be used as a signal processor. The advantages of spectrum analysis as the signal processing method are highlighted.The laws of geometrical optics applied to the present scattering problem provide a relationship for the frequency of the collected signal which is expressed as the sum of two terms, the conventional Doppler frequency and the "anisotropic frequency", which is directly dependent on the particle size. These theoretical assertions were examined experimentally. Measurements on glass and metal particles of known diameters showed good agreement with the theory.
    Additional Material: 9 Ill.
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  • 25
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 70-73 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A primarily experimental investigation of the deposition of droplets from a turbulent two-phase suspension flow on a parallel vertical wall has been found to be closely related to the ratio of fluctuation velocity of the droplets to that of the flow and the size of the droplets. Data are obtained for an air-water mist flow parallel to a vertical flat plat at Re = 1.54 × 105 to 4.2 × 105 by the use of a particle-sizing two-dimensional reference-mode laser-Doppler anemometry technique. Although no rigorous theory can be formulated at present due to the complexities involved, however, an analytical attempt is made in the hope of providing an explanation to the physics of the phenomenon. It is based on an apparent turbulent viscosity of the fluid as felt by the moving particles in a turbulent two-phase suspension flow and the most energetic eddy frequency of the flow.
    Additional Material: 4 Ill.
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  • 26
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 54-59 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Predictions of the droplet size and velocity distributions in sprays under isothermal conditions are reported. The calculations are based on the maximum entropy formalism, complying with the conservation laws of liquid mass, momentum and energy. This theoretical approach considers only the macroscopic quantities about the atomization processes, without resorting to the details of the liquid breakup processes such as the onset and growth of instabilities. The derived joint droplet size and velocity distribution function depends on the Weber number as well as the liquid mass, momentum and energy source terms.These parameters represent the conditions under which the atomization occurs. The droplet velocity distributions are truncated Gaussian distributions for any specific sizes. The nondimensional Sauter mean diameter decreases slightly with the Weber number and then approaches an asymptotic constant. The calculated values of D21/D30 are very close to unity which agrees with the experimental observations. The computations also show that the atomization efficiency is very low; less than 2.6 percent.
    Additional Material: 8 Ill.
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  • 27
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 60-69 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This paper describes experimental measurements and numerical predictions of the motion of particles of size 500-800 m̈m diameter in a 20 m long (i. e. 620 pipe diameters) vertical tube. The numerical simulations suggest that the particles attain a fluctuating r.m.s. velocity in a direction normal to the axis of the tube which is at least one order of magnitude less than that of the gas phase turbulence fluctuations. However, the measured values are of the same order as the gas phase turbulence fluctuations (i. e. 0.5 to 1 m/s). This discrepancy is likely to occur because of particle/wall interactions and these were investigated in separate experiments. Although the cause of the measured coefficients of restitution in the normal direction being greater than unity was not finally demonstrated, the results indicated strongly that the effects were due to non-ideal bouncing of the particles in the presence of particle spin.
    Additional Material: 11 Ill.
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  • 28
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 74-79 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The use of very simple one-parameter models of particle interactions for the analysis of the concentration dependence of the collective diffusion coefficient as determined by photon correlation spectroscopy is illustrated by measurements on two different systems. In one, a micro-emulsion, attractive interactions are dominant whereas in the other, a silica dispersion, repulsive interactions play the major role.
    Additional Material: 4 Ill.
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  • 29
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 107-112 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Given the paucity of optical methods for sizing nanoparticles (those between 1 and 100 nm), more methods are needed if, as has been predicted, such particles have a bright future. Linearly polarized light is transformed into elliptically polarized light upon scattering by small spheres at 90°. The resulting circular polarization increases as the fifth power of particle diameter and the shift of the azimuth of the vibration ellipse from the vertical increases as the square if the particles are negligibly absorbing. Titanium dioxide spheres (in air) with diameters between 20 and 120 nm give circular polarizations between about 10-5 and 10-1 for incident light of wavelength 450 nm. The corresponding azimuth shifts (in radians) lie between about 10-2 and 1. These values are within reach of experimental techniques based on polarization modulation. Metallic spheres yield much larger circular polarizations and azimuth shifts (with signs opposite those for negligibly absorbing spheres), both of which increase approximately as the square of particle diameter.
    Additional Material: 4 Ill.
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  • 30
    Electronic Resource
    Electronic Resource
    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 160-168 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: High-pressure injection fuel sprays have been investigated in a single-cylinder research Diesel engine using the laser and phase Doppler anemometry techniques to measure fuel droplet velocities and sizes and their spatial and temporal distributions within the spray. The measurements relate to the determination of the droplets' axial velocity component and diameter on the spray centre line between 75 and 100 nozzle diameters downstream from a single-hole injector nozzle. The experimental program covered the use of both Diesel and a non-combusting alcohol fuel. Measurements at radial locations in the spray and at different fuel loads were also taken for the alcohol fuel. Temporally resolved measurements of droplet velocity and size are presented together with time  -  averaged values in such a way as to isolate the contributions from the leading and trailing regions of each spray and identify two different break  -  up mechanisms occurring as suggested by a conceptual model of the spray behaviour.
    Additional Material: 11 Ill.
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  • 31
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 144-151 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A basic requirement of particle size analysis through sedimentation is the perfect dispersion of the particles in suspension. The dispersion must be perfect and stable. To ensure this, for a number of solids DIN 66111 specifies sedimentation liquids and suitable dispersing agents and defines an upper limit for the concentration of the solids in suspension. Some instruments require higher solids concentrations than are recommended in DIN 66111. However, there is no simple test to prove the stability of a dispersion with sedimenting particles.An effective method for testing the stability of a dispersion is to make a number of simultaneous sedimentation analyses, measuring the concentration of the particles at different distances from the surface of the liquid. If the dispersion remains perfect, identical particle concentrations have to be measured, when the measuring time is normalized to one distance from the surface (e.g. t1′ = t(h3/h1), t2′ = t(h3/h2) …). From the particle concentration, distance from the surface and time, the particle size distribution can be calculated.If the results of the lower (and hence later) measurement show a shift to the larger diameters, agglomeration has occurred. If the sensing technique is light extinction, then the effect is particularly pronounced.A photosedimentometer with three light beams at distances from the surface of 1.5, 15 and 150 mm was used to demonstrate the effect of agglomeration on particle size distribution and to optimize sedimentation liquids and dispersing agents. An attempt was made to determine the kinetics of agglomeration from the increase in transmission of a light beam through a suspension.
    Additional Material: 9 Ill.
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  • 32
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 152-159 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A confined jet flow involving glass particles was examined to clarify fundamental aspects of the turbulence structure of two-phase flow. Spherical glass particles of mean diameter 62.4 m̈m were loaded in a primary jet at a mass loading ratio of 0.3. The primary jet diameter was 13 mm and exit velocities at the centre line were set at 20 and 30 m/s. The confined pipe diameter was 60 mm and velocities were set at 10 and 15 m/s. The particle and gas flow characteristics, such as local mean velocities, their fluctuations and size distribution, are discussed for three flow conditions which were obtained by changing the velocities of primary and secondary flows.Laser Doppler anemometry was applied to measure the flows of both particles and tracer, discriminated by scattering light intensity, and the precise particle size, for examining the dependence of particle size on the flow, by phase Doppler anemometry. The signal processing of the phase Doppler anemometer was based on a fast Fourier transform method to detect not only Doppler frequency for velocity but also the phase shift of Doppler signals for particle sizing. The processing system consisted of conventional fast analogue to digital converters, multi-digital signal processor units and a host microcomputer.
    Additional Material: 17 Ill.
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  • 33
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 242-247 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The kinetics of batch grinding quartz from a feed of 600 by 425 m̈m to a product of 80% less than 10 m̈m have been determined using screening and laser diffractometer sizing for size analysis. The specific rates of breakage decreased by a factor of about three when the material became less than about 100 m̈m in size, but the primary breakage distribution function also changed to give proportionately more fine material, so that the grinding efficiency expressed as the development of surface area (B.E.T.) per unit of energy input did not decrease. Analysis of the shape of the particles in the 25 × 38 m̈m size range showed that particles of this size produced by roll crushing or by 8 minutes of grinding of a 425 × 600 m̈m feed were not different but at long grinding times the particles were rounded. This suggests that the breakage mechanism changes to give more chipping and abrasion and less disintegrative fracture. As the material approached the ultrafine size range it adhered to the mill case and there was no further size reduction. However, a technique for striking the mill case to dislodge the particles was successful in allowing further grinding to 40% by weight less than 2 μm.
    Additional Material: 12 Ill.
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  • 34
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 256-256 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 35
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 248-249 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Generalized Lorenz-Mie theory (GLMT) is validated by comparisons between theoretical results and experimental optical levitation data. Selected results are presented.
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  • 36
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 256-256 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 37
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 250-255 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The bipolar diffusion charging process is studied theoretically for aerosol particles in high purity argon and nitrogen. The Fuchs theory is extended by the incorporation of the free electron charging of the aerosol particles. The ion parameters for positive and negative ions are assumed to be identical. The influence of the free electrons explains the differences between the mean mobility and mean mass of negative and positive ions. The ratio of the electron number concentration to the number concentration of negative ions is used to fit the curves, calculated by the extended model, to the experimentally determined bipolar charge distribution in argon and nitrogen. The extended Fuchs model was found to be rather insensitive to variations in the mobility and mass compared with the model with four different ion parameters. Further experimental studies of the bipolar charge distribution in a gas mixture of pure nitrogen and sulfur hexafluoride, SF6, indicate the importance of the free electrons in the bipolar diffusion charging process.
    Additional Material: 4 Ill.
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  • 38
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 6-10 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is well known that broadening of the observed particle size distribution occurs both at the finer end and at the coarser end of the distribution when using the Coulter Counter. This problem can partly be overcome with the aid of electronic pulse editing. However, it has been found that the accuracy can be further improved when the Coulter Counter is equipped with a hydrodynamically focused (HDF) aperture. The standard deviations of the main peaks of samples with diameters of 5.0, 10.2, 15.1 and 20.0 m̈m decreased by 21%-49% with HDF. HDF also prevents artefacts at the fine side of the main peak that originate from particles re-entering the sensing zone of a standard aperture after they have passed through it. In the experimental model used i.e. a silica sample with a diameter of 15.6 m̈m, the estimate of small particles (〉10 μm) decreased from 6.5% to 0.4%.
    Additional Material: 5 Ill.
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  • 39
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 11-15 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The electrical sensing zone technique is long established, well researched and widely used. It is often used as a reference method against which others are compared or calibrated. This position should not be allowed to disguise the potential which exists for still greater accuracy and versatility. In this paper the use of the hydrodynamic focussing technique is evaluated and an experimental comparison is made with a normal Coulter stand for several samples. It is clearly shown that hydrodynamic focussing enables higher resolution and accuracy to be obtained for materials with narrow or unusual particle size distributions.
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  • 40
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 97-97 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 41
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 87-92 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The principal focus in this paper is the development of a general method to simulate irregulary shaped particles whose perimeters are fractal. It is shown that this method can produce a particle of almost arbitrary fractal dimension. The Fourier components of these fractals are then computed. It is shown that these components were either independent of the fractal dimension or that any dependence is less important than other properties of the cluster such as symmetry and aspect ratio.
    Additional Material: 7 Ill.
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  • 42
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 93-96 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A theoretical model for the interaction of charged particles with an alternating current field is developed. This model permits the determination of the particle size distribution by a numerical nonlinear iterative method. Results of numerical simulations are presented and discussed. Restrictions on the applicability of the model as an on-line measuring system are pointed out.
    Additional Material: 6 Ill.
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  • 43
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 80-86 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Inversion of the Laplace integral equation, used in the laser scattering measurement of colloidal particle size distributions, presents sever numerical and experimental difficulties. In the presence of noise the variance of the inversion integral is infinite, indicating maximum uncertainty in the accuracy of the inversion. The regularized inversion of the Laplace intergral equation provides a convenient computational algorithm which requires no a priori knowledge of the unknown linewidth distribution. Using the eigenfunction decomposition of the Laplace kernel, the spectral properties of the regularized inversion may be seen.Regularized inversion represents a type of low pass filter which preserves the properties of the inversion spectrum at low frequencies, but provides a cutoff at a point controlled by the regularization parameter. This filtering reduces the variance of the inversion to a finite value. Regularized inversion is somewhere between optimal filtering and the abrupt truncation used in singular value decomposition and other similar methods. Two examples, a monodisperse and a bimodal linewidth distribution, are used to compare the performance of regularized inversion to that obtained through an optimal filter.
    Additional Material: 7 Ill.
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  • 44
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    Weinheim : Wiley-Blackwell
    Particle and Particle Systems Characterization 7 (1990), S. 113-115 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Using computations based on Mie scattering theory, the influence of the size and shape of the receiving aperture on the signal properties of a phase/Doppler system is examined. For circular apertures exceeding a certain size limit, it is shown that the signal phase is non-monotonic with respect to the particle diameter and exhibits abrupt changes of 180° at certain values of the diameter. This difficulty may be overcome by using rectangular apertures with appropriate aspect ratios.
    Additional Material: 7 Ill.
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  • 45
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    Particle and Particle Systems Characterization 7 (1990), S. 191-202 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2 PHF) formulations and modelling techniques is introduced. Basic theorems for the case of dispersed 2 PHF are presented. Phase interaction terms with a clear physical meaning enter the equations and this formalism provides some guidelines to avoid closure assumptions or to close those terms rationally. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations can be rigorously and systematically obtained with this methodology in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that the dispersed phase is well described by a "Boltzmann-type" equation and Eulerian "continuity", momentum and fluctuating kinetic energy equations for the dispersed phase are obtained. A k-ε turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy. Closure assumptions are proposed for the phase interaction terms. This model is then used to predict the behaviour of an axisymmetric turbulent jet of air laden with solid particles varying in sizes and concentrations. Numerical results compare reasonably well with available experimental data.
    Additional Material: 14 Ill.
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  • 46
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The paper describes the application of a stochastic separated flow model for the dispersed phase to the prediction of a particle-laden turbulent air jet discharging at 13 m/s from a 15 mm nozzle into stagnant surroundings. Emphasis is placed on the stochastic element of the Lagrangian particle tracking part of the model and on the importance of particle initial conditions over the first 20 jet diameters. Calculations are presented for 80 m̈m sized glass particles which clarify how particles with turbulent Stokes number less than unity acquire axial turbulence much larger than radial. Far from being only a response to the gas-phase turbulence as implied by the model, the axial turbulence is shown to be also produced by an interaction between particle radial turbulence fluctuations and cross-stream spatial gradients in particle mean velocity, here referred to as "fanspreading". In addition, initial particle turbulence levels remain identifiable for about 10 jet diameters; the initial radial turbulence reinforces the fan-spreading contribution and leads to extra generation of axial turbulence farther downstream. In general, the results agree well with experimental measurements.
    Additional Material: 3 Ill.
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  • 47
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The intensity angular pattern of the light scattered by a drop at a scattering angle of ca. 90° is related to the size of the scattering drop. A simple relationship between the number of fringes per degree and the size is presented. The possibility of measuring the drop size through visualization of the fringe pattern is demonstrated.
    Additional Material: 6 Ill.
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  • 48
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    Particle and Particle Systems Characterization 7 (1990), S. 209-220 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The measured velocity fluctuation of particles in dispersed twophase flow systems is discussed and an interpretation of particle velocity statistics is given. Besides the turbulent velocity fluctuations resulting from the particle's response to the fluid turbulence, two additional apparent fluctuation components may be distinguished, caused by inertial effects of the particles and by a polydisperse particle phase.Especially for larger particles inertial effects may become important and therefore the particle motion in the flow field is strongly governed by the inlet conditions, namely the instantaneous particle velocity. Therefore, the measured axial particle velocity fluctuation at a given location may be considerably increased as particles from different starting locations with different initial velocities may cross the same measuring point. This dynamic particle behaviour is demonstrated by the numerical simulation of particle trajectories in a given flow field. The results show the importance of including appropriate inlet conditions for the numerical prediction of particulate two-phase flows.Further, in experimental realizations of particulate two-phase flows, the particles usually exhibit a certain size distribution. Owing to the different responses of the different sized particles to both the mean flow field and the turbulence characteristics of the flow, the measured particle velocity fluctuations are higher than in the comparable monodisperse case. Therefore, the particle size distribution was taken into account in the present numerical calculations in order to obtain results which are comparable to the corresponding experiments. In this numerical simulation the particle mean velocity and the rms value of the velocity fluctuation were obtained by averaging over the whole particle size distribution and then compared with the measured values. Calculations are presented for two different shaped particle size distributions with a different mean size and compared with calculations with a monosized particle material and experimental results.Further, the behaviour of the different sized particles in the particle size distribution is discussed by considering the changes in the particle size distribution and the particle velocity distribution throughout the flow field.
    Additional Material: 9 Ill.
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  • 49
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Pulse holography and the phase-Doppler technique are two of the very few methods with which the size and velocity of individual particles within a two-phase flow may be simultaneously measured. This enables the two-dimensional frequency distributions of particle size and velocity to be compiled and allows the existence of mutual correlations to be verified.The application of both methods to investigations into water droplet collections within the hollow spray cone of a swirl pressure-jet atomizer is described. When comparing the results of measurements obtained by the two methods under identical conditions, one fundamental difference must be taken into account: whereas pulse holography delivers space-averaged concentration-dependent frequency distributions, those derived from the phase-Doppler technique are time-averaged fluxdependent. The methods hence deliver different, but equivalent, results. Since the possibility of conversion exists, both representations are always available. As far as the particle size distributions are concerned, the results obtained from the two methods confirm the expected differences, whilst verifying the compliance of the interconverted size distribution data. Regarding the velocity distributions, however, some unexplained discrepancies still remain.
    Additional Material: 11 Ill.
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  • 50
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    Particle and Particle Systems Characterization 7 (1990), S. 233-241 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Mean particle diameters are important for the science of particulate systems because they provide information on particlesize distributions in such a way that they can be related to physical or physiological processes or product properties. There are different notation systems for such mean diameters which may cause much confusion. This equally applies to their nomenclature. The present paper is concerned with comments on the “Moment-Ratio” and German (DIN) notations. The Moment-Ratio notation is recommended for standardization. A more extensive contribution of statistics to the science of particulate systems is recommended.
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  • 51
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The analysis of particles in the sub-micron range by sedimentation field flow fractionation (SFFF) is not new, but its commercial exploitation is recent. This inevitably will lead to a rigorous evaluation of the technique by many laboratories, for many applications, as well as to rapid development.This paper describes first an evaluation of the new commercial instrument using both ideal and real materials. These experiments lead to a discussion of the software package and of the influence of experimental conditions. A particular study is described of the combination of the SFFF technique with that of quasi-elastic light scattering. The paper concludes that SFFF now offers the technology for realistically measuring particle size distributions at high resolution in the submicron size range. The analysis time is in the order of one hour, but can be reduced at the expense of resolution.
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  • 52
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    Particle and Particle Systems Characterization 7 (1990), S. 116-120 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: It is shown that if the pinhole in a phase Doppler system' s collection optics is misaligned, even by a matter of micrometers, the effective collection aperture will be different from the aperture of the collection lens. This directly alters the phase characteristics of the resulting signal and can produce systematic and random errors in drop size measurements. The results of misalignment in a simple system are calculated, experimental evidence of the errors presented, and it is shown that replacing pinholes with vertiacl slits will reduce the sensitivity to such errors.
    Additional Material: 7 Ill.
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  • 53
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    Particle and Particle Systems Characterization 7 (1990), S. 171-180 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Numerical predictions of two-phase turbulent gas-particle flows are reported for two test cases: for a plane jet and for an axisymmetric free jet. The numerical algorithm uses an Eulerian approach for the fluid phase and the particulate phase is described by using a Lagrangian stochastic model. The k-ε turbulence model was used to characterize the length and time scales of the fluid. In the plane confined jet the influence of the restitution coefficient on the statistical distribution of velocities was analysed. Particular attention was dedicated to the ε equation corrections regarding the problem of the free jet spreading rate overprediction. The influence of the particle tangential momentum equation on the prediction of particle concentration near the centre line in axisymmetric free jets was also analysed. Comparisons between predictions and experimental data are presented and shown to be satisfactory regarding the incomplete knowledge of turbulent multiphase flows.
    Additional Material: 13 Ill.
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  • 54
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    Particle and Particle Systems Characterization 7 (1990), S. 181-190 
    ISSN: 0934-0866
    Keywords: Chemistry ; Industrial Chemistry and Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A Lagrangian model of particle motion in turbulence has been developed. The model is stochastic in the sense that the "instantaneous" fluid velocity field is generated from known turbulence energy and time scales of large eddies by using a random sampling. The particle motion during the interaction with the eddies is deterministic as being predicted from solutions of Lagrangian momentum equations. On the basis of a large number of calculated trajectories, the distributions of local particle mean and fluctuation velocity components and of the mean square particle displacement are evaluated in a flow domain. The results of the predictions for the case of particle dispersion in nearly homogeneous and isotropic turbulence behind a grid are compared with existing experimental data and satisfactory agreement is achieved. The model is also applied to the case of the particle dispersion from a point source in a nonhomogeneous turbulence of fully developed pipe flow. The agreement with experiments is satisfactory for both heavy and tracer particles. An explanation is given for the experimentally observed phenomenon that in some cases heavy particles disperse faster than fluid points.
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  • 55
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 37-55 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fully automatic three-dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular - the octree and Delaunay approaches - have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide-and-conquer approach of the octree method with the simplicity and optimal properties of the Delaunay triangulation.
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  • 56
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Adopting an updated Lagrange approach, the general framework for the fully non-linear analysis of curved shells is developed using a simple quadrilateral C0 model (HMSH5). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with large rotations in space, finite stretches and generalized rate-type material models. In particular, a geometrically exact scheme for configuration update is developed by making use of the so-called exponential mapping algorithm, and the resulting element was shown to exhibit a quadratic rate of (asymptotic) convergence in solving practical shell problems with Newton-Raphson type iterative schemes. For the purpose of updating the spatial stress field of the element, an ‘objective’ generalized midpoint integration rule is utilized, which relies crucially on the concept of polar decomposition for the deformation gradient, and is in keeping with the underlying mixed method. Finally, the effectiveness and practical usefulness of the HMSH5 element are demonstrated through a number of test cases involving beams, plates and shells undergoing very large displacements and rotations.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 483-514 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non-symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near-incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 599-617 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This study, dealing with model reduction for thermal diffusion, describes the numerical techniques used: the Eitelberg, Marshall and aggregation methods. The non-linear model of a heat transmission tube, to which these methods are applied, is then described, pointing out the necessary initial algebraic treatment for reduction. Finally the outputs of the complete model and of several reduced ones are compared for some characteristic variations of the inputs. For this problem, the Eitelberg and Marshall methods, which can be used with a high coefficient of reduction, are well adapted.
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  • 59
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 699-717 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Finite Element Iterative Method (FEIM) is extended to the analysis of asymptotic fields of materials with non-linear behaviour. It is used in the investigation of the asymptotic field of an interfacial crack of power law hardening materials. The material is assumed to deform according to the total deformation theory of plasticity. The results of the analysis provide evidence to support the hypothesis that the asymptotic field can be cast in the form of the HRR-singularity multiplied by a function of the product form. This function can be written as a series of oscillatory functions, similar to those encountered in an elastic field, each of which is valid over a substantial range of the process zone. The real part of these terms depends on the loading mode, process zone size as well as material properties; it is, however, very small compared to the HRR-singularity. The imaginary part which gives the phase shift is much smaller than the elastic value and is a weak function of the hardening power and the size of the process zone of interest; it eventually vanished at extremely small distances.
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  • 60
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 775-783 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Force fields computed directly from strains calculated in a displacement type finite element description of a structural element of varying sectional rigidities show extraneous oscillations. The origin of these oscillations is traced to the fact that the displacement type finite element procedure determines strains derived from the displacement field in a least squares correct sense and that force resultants computed using these strain fields and the actual sectional rigidities result in unwanted oscillations. It is necessary to introduce the concept of redistributed assumed force resultant fields that maintain a ‘consistent’ relationship to the strain fields and also are orthogonal to these strain functions. In this paper, the Hu-Washizu theorem is invoked to justify the introduction of an orthogonally correct reconstituted assumed force resultant field which will then be free of extraneous oscillations. The quadratic isoparametric tapered bar element serves to illustrate the underlying principles.It follows that the extremely general Hu-Washizu principle is the most practical procedure of implementing an assumed force resultant, assumed strain displacement type formulation to introduce consistency and thereby remove problems associated with field-inconsistency (such as cause locking in constrained media elasticity) and force resultant oscillations due to varying sectional properties.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 801-809 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New 8-node solid elements with two parallel faces and one traction-free cylindrical surface are derived using the assumed stress hybrid model. Six new expressions of stress components are developed by using four stress functions and cylindrical co-ordinates, so that the normal stress σz on the plane perpendicular to the two parallel faces varies as a parabola, and the assumed stress field satisfies the equilibrium equations as well as the traction-free conditions over the cylindrical boundary. The assumed stress field also satisfies the compatibility conditions when the new element is degenerated into the 2-dimensional case. Examples have clearly demonstrated that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress σz.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 861-880 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Explicit integration across the thickness for three-dimensional degenerated shell finite elements is analysed. For this purpose a modifed formulation is proposed. The Jacobian matrix of the physical-parameter spaces transformation is decomposed into a product of ‘in-middle-surface’ and ‘out-of-middle-surface’ terms. This enables an expansion to be carried out of the strain-displacement matrix into power series of the thickness variable. Explicit integration is then performed and the corresponding formulae of the stiffness and mass matrices are given. The possibility of ‘locking’ for thin structures is explained. The analysis is applied to homogeneous and multilayered structures. Numerical applications for linear problems are given in the last part of the paper.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 913-933 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Non-linear responses of dam-reservoir systems are not well understood, because of the lack of an exact time-domain solution for the far field (extending to infinity) of the fluid. This paper presents a procedure for efficient time-domain analyses. It is based on a semi-analytical solution and is suitable for the determination of the interactive behaviour of dam-reservoir systems.In this formulation, the fluid domain is divided into a near (to the dam) field, which is finite, and a far field extending to infinity. Arbitrary shapes of the upstream face of the dam, and of the bottom of the reservoir floor in the near field, are presumed. Furthermore, the far field is assumed to have a constant depth. The irregular near field is modelled by using the finite element method. A time-domain semi-analytical solution is obtained for the far field. For a vertical dam subjected to earthquake and ramp loadings, numerical solutions obtained compared well with the piecewise exact form of the analytical solution.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1003-1020 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An improved formulation for solving 2D transient scalar wave propagation problems by the Boundary Element Method (BEM) is presented. The kernels presented are simpler and better behaved than those that have appeared in the published literature. An appropriate set of temporal shape functions for linear variation is used. For spatial variations isoparametric quadratic elements are used. All of these represent significant improvements over the present level of sophistication in the analysis of 2D transient scalar problems. The algorithm is implemented in a general purpose boundary element code known as GPBEST.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1049-1063 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new method of modelling the radiation effect in a time-domain finite element analysis of semi-infinite solids is proposed. The domain to be analysed is divided into a finite, interior region and a semi-infinite, exterior region. The standard finite elements are used to model the interior region. An infinite element is used to model the semi-infinite region. The main feature of the proposed method is the selection of semi-infinite shape functions to develop the infinite element. A procedure is proposed whereby the necessary shape functions are derived directly from frequency-domain analytical mode shapes. The interior and exterior regions are coupled by enforcing displacement continuity at the interface. The validity of the method is demonstrated in this paper by analysing a two-dimensional, linear (damped), anti-plane, shear-wave (plane Love-wave) propagation problem. The results obtained by the proposed method are compared with those obtained by direct finite element analysis with a fixed boundary placed sufficiently far from the location of loading to avoid wave reflections.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 141-159 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right-hand sides. The versions of the method proposed in the past treat the right-hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 197-209 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly.The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 449-452 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 473-482 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non-linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 453-472 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 559-578 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity.The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 647-663 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non-linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.
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    Notes: This report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid. The equation of motion governing the inviscid fluid is expressed in terms of the displacements. This ensures that compatibility and equilibrium will be satisfied automatically along the interface of the coupled systems. To suppress circulation modes with non-zero energy, reduced integration is used when computing the element stiffness matrix contributed by the fluid. In addition, a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration. Numerical examples for both fluid and coupled fluid-solid systems are performed and the results are shown.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 755-774 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present paper deals with the application of the finite element method to dynamic contact buckling problems. The penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial-and-error method is employed to obtain the converged contact state. Numerical examples are analysed to show the effectiveness and the validity of the method, and it is applied to a dynamic buckling problem involving contact phenomena.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 811-831 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The dynamic interaction between a compliant material and an impulsive pressure field, periodic in space and instantaneous in time, was examined as a first step at modelling the interaction between organized structures in a turbulent boundary layer and a compliant surface. The interaction, modelled two-dimensionally, was treated dynamically by matching the pressure forces to the surface stresses in the compliant material at each instant of time. A new boundary element method was formulated to model the compliant material which was treated as a linear isotropic material, elastic in dilatation and viscoelastic (Standard) in shear. The inertial forces and viscoelastic creep stresses have been included in this formulation as transient body forces. The elastic interaction was characterized by a non-dimensional threshold velocity, above which the elastic instabilities grew temporally and spatially in the downstream direction to produce a non-linear breakdown of the interaction. Freestream velocities as high as 9CT (shear wave speed) were found to produce stable elastic interactions. Thinner materials produced smaller amplitude waves of higher frequencies that grew more rapidly than those in thicker materials. The stability characteristics were independent of the location of the compliant material with respect to the spatial distribution of the pressure pulse. For viscoelastic interactions, the stability curve, which serves as a bound on the types of materials capable of producing drag reduction, shows distinct regions of elastic types of interactions (Class B) and damping dominated interactions (Class A) as a function of the constants of the rheological model describing the compliant material. Class A disturbances in these interactions show slower growth or decay than Class B disturbances.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 909-912 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 953-968 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The coupled thermoviscoelastic response of a solid-fluid system is computed by a finite element formulation which involves only temperature and displacement fields. The Laplace transform with respect to time is applied to the coupled equations. This results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution. Also, this formulation permits the use of fractional derivatives to model viscoelastic material behaviour.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 935-951 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element (FDE) formulation. Closely related to the subspace forward iteration method, the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems, takes full advantage of the banded configuration of the stiffness, inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs. A shifting technique for convergence acceleration and an eigenpair verification scheme are also presented. Numerical examples are shown demonstrating the excellent performance of the solution procedure.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1021-1031 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An integral solution method based on the concept of the direct boundary element technique has been applied to develop a solution procedure for problems of diffusion with a non-linear reaction in one dimension. The non-linearity is handled by a process of quasi-linearization over subintervals or elements in the main domain of integration. The weighting functions are defined for each subinterval such that the discretization is exact for the corresponding linear problem. This leads to a new powerful and simple method for the solution of this class of problems. A banded global matrix is obtained with both the concentration and its gradient as the unknown variables, and the problem is solved in an iterative manner. Illustrative results are presented for a test problem of diffusion with a second order reaction in an infinite slab, an infinite cylinder and spherical geometries. The accuracy of the method for situations with a sharp concentration gradient is demonstrated. The technique can also be used to numerically compute the solution in the boundary layer for fast reactions.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1079-1094 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An approach, which is based on the double porosity concept and takes into account pore deformation, has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media. This approach has resulted in a set of non-linear (variable coefficient) differential equations. Various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters. The finite element technique has been employed as the numerical tool for the solution of these equations. The results based on the proposed non-linear formulation have been compared with those of previously presented linear (constant coefficient) formulations. It is found that, in relatively rigid formations, the linearity assumption is quite reasonable and can successfully model the behaviour of fissured porous media. However, in very deformable formations, the linearity assumption could lead to a significant level of error in the numerical solutions.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1109-1130 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several kinds of implementation, using various numerical techniques, are proposed. Validations of these implementations and comparisons between them are investigated by means of a set of simple but comprehensive examples.
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1159-1175 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The treatment of ageing processes in polymers by the finite element (FE) method is described. The development of this analytical method is motivated by the need to assess the effects of ageing on the structural performance of polymers and polymeric composites, particularly when the structures are large and expensive to replace. Also, there is a need to assess the effectiveness of corrective action options when ageing problems do occur, which can be treated by this method. The method describes the treatment of multiple, reactive chemical species in multi-layered polymeric materials by the finite element method. Example problems featuring the simultaneous diffusion and chemical reaction are illustrated: a simple problem of binary diffusion and reaction with comparison of numerical to exact results, and the staged ageing/structural analysis of a solid rocket motor.
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  • 83
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1281-1298 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An effective and efficient error estimation scheme for finite element plate and shell analysis is presented. The error estimate method proposed is applicable to all the plate and shell elements developed using either classical plate and shell or continuum mechanics theories. The global error in energy norm is computed by summing all the elemental errors. The method is well suited for adaptive mesh refinement as the error contribution for each element is known. Demonstration examples using uniform and adaptive refinement schemes for both the plate and shell analysis show the effectiveness of the method proposed.
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  • 84
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1299-1321 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A triangular mesh generator is presented which makes extensive use of side swapping and mesh smoothing to create a grid with few obtuse triangles. To perform the above task a data structure is presented which holds full adjacency information both for nodes and elements. It is shown how this data structure is employed in the process mesh generation, and how the methods of computational geometry such as region decomposition are used not only to decompose a complex region, but also to reflect the boundary grading into the interior the region. Algorithms are provided to show the mechanism of these processes and practical examples are given to support the approach.
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  • 85
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1343-1358 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of characteristics is combined with the method of least-squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split-operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection-dispersion simulation.
    Additional Material: 7 Ill.
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  • 86
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1441-1454 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional approaches for computational structural dynamics (CSD) relevant to time-integration methods involve first employing the classical Galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employing finite difference approximations for deriving the appropriate step-by-step algorithms. And, almost all of the widely advocated (existing) step-by-step schemes for structural dynamics require an initial acceleration vector to be specified (evaluated) in addition to displacement and velocity vectors for starting the schemes. Unlike the above, in this paper we introduce new representations and architecture towards providing not only direct self-starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics. Thereby, a robust and effective methodology of computation is presented which is an extension of our previous efforts (see Tamma and Namburu3). In particular, to illustrate the basic concepts, in this paper we focus attention on the development of explicit time-integration formulations. The methodology involves expressing the governing dynamic equations of motion in conservation form, and firstly temporal discretization is accomplished in the spirit of Lax-Wendroff-type formulations. Therein, discretization in space is accomplished by introducing stress-based representations and employing the classical Galerkin scheme, and, quite naturally, we advocate employing finite elements as the principal computational tool because of its several inherent advantages. The stability and accuracy of the proposed formulations and the several added distinguishing features are briefly highlighted. Considerations on the effects of damping are additionally included and the introduction of general boundary conditions in a natural setting permits an effective generalized architecture for general applications. Numerical test models are presented to validate the overall developments for computational structural dynamics.
    Additional Material: 9 Ill.
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  • 87
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1501-1526 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE-calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.
    Additional Material: 39 Ill.
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  • 88
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1551-1567 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the development of an automatic, two-dimensional, quadrilateral element mesh generator. The methodology is based on the looping algorithm developed in part by Dr M. L. C. Sluiter. Bezier curves are used to define the boundaries of the parts to be meshed. The required interaction by the user is reduced to specifying the boundary geometry, the preferred element size and the refinement coefficient. Transition elements are automatically generated between regions of varying element sizes. The ability to offset specified boundary curves insures well-conditioned elements along the boundary. Meshes for several sample geometries are presented to illustrate the versatility of the mesh generator.
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  • 89
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1595-1638 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame-work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece-wise constant functions and be L2-ortho-gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non-linear analysis.
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  • 90
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1701-1714 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation of temperature distributions for systems exchanging radiation heat requires as a first step the determination of the heat fluxes caused by radiation at its surfaces. The functional of the variational principle is the starting point of a numerical solution method.By using finite element procedures a system of linear equations is derived, which supplies an approximation of the radiosity. Having the radiosity, the heat flux at the surfaces, which governs the boundary condition for the temperature distribution in the structure, can be calculated. A method of determining the view-factors using the concept of the finite element method is also given.
    Additional Material: 6 Ill.
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  • 91
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 1797-1797 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 92
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 1-12 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an application of linear programming for the analysis of plane strain rigid-plastic flow. First, linear programming and the theory of a rigid-plastic material are briefly revised. The implementation of linear programming for rigid-plastic flow is then described. The method is to subdivide the material into rigid triangular blocks which may slide upon each other, dissipating energy at a rate proportional to the rate of sliding. Many different modes of deformation are possible; linear programming is used to select the mode that gives the least rate of total energy dissipation. The indentation of a strip by blunt-nosed indenters is used as an example. Results of the linear programming method are compared with the exact slip line field solutions.
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  • 93
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 99-113 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Procedures for extending the useful scope of the finite difference method in solid mechanics applications are presented. The improvements centre around the introduction of the physical nature of the deformations into the equations used to formulate the approximate solution. This is accomplished by evaluating the coefficients of Taylor series expansions for the displacement approximations in terms of rigid body motions, strains and derivatives of strains. This procedure is demonstrated with plane stress applications. The ability to interpret the derivative approximations physically allows the fictitious nodes typical of the finite difference method to be rationally incorporated into the model as a means of enforcing traction boundary conditions. An example problem is solved using both regular and irregular meshes. The displacements and stresses compare well with finite element solutions.
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  • 94
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 201-205 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 95
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 821-831 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical tools for simulating the casting process are employed in an increasing manner by foundry engineers in order to understand and improve casting techniques. The correct simulation of metal flow and temperature profiles during filling is an important part of an overall numerical simulation kit which includes solidification and residual stress evaluations.In this study, we develop a two-dimensional finite element model for studying metal flow and temperature fields during filling of mould cavities. A proper choice of turbulent/laminar model, correct tracking of metal free surface and evaluation of temperature to include metal-air-sand interaction are some of the essential features of the model.
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  • 96
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 833-858 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite shell element for layered fibre reinforced composite shells has been developed. The degeneration principle is used in combination with specific kinematic assumptions. The thermo-elastic material is either described by the behaviour of the local components, i.e. fibre and matrix material laws and geometrical configuration in each layer, or by the overall orthotropic layer material laws.Thickness integration for obtaining the different contributions to the shell element's stiffness matrix is performed analytically and prior to the numerical in-plane integration. This leads to a considerable saving in computer time during the incremental-iterative analysis.Geometrical non-linearities in terms of large deformations and material non-linearities in terms of layer craccking are taken into account. Accompanying eigenvalue analyses allow the determination of the - sometimes rather complicated - buckling behaviour with non-linear prebuckling deformations.
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  • 97
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 875-898 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The aim of this paper is to categorize the major fixed grid formulations and solution methods for conduction controlled phase change problems. Using a two phase model of a solid/liquid phase change, the basic enthalpy equation is derived. Starting from this equation, a number of alternative formulations are obtained. All the formulations are reduced to a standard form. From this standard form, finite element and finite volume discretizations are developed. These discretizations are used as the basis for a number of fixed grid numerical solution techniques for solidification phase change systems. In particular, various apparent capacity and source based enthalpy methods are explored.
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  • 98
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 899-914 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical study of three-dimensional natural convection with phase change in a rectangular parallelepiped is described. The fluid has temperature-dependent variable properties. The governing equations are approximated by finite differences, second order in space and first order in time. A boundary-fitted co-ordinate system is implemented to predict the shape and the movement of the solid-liquid interface. Preliminary results have been obtained for freezing of water in a cube for Rayleigh numbers in the range of about 105-106.
    Additional Material: 6 Ill.
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  • 99
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 391-395 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 100
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 371-387 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element algorithm which can be used to model either linear or non-linear viscoelastic material behaviour is described. The algorithm is verified for the linear case by comparing numerical and analytical solutions for (a) a uniaxial tensile specimen, and (b) an infinite plate with a hole subjected to a remote uniaxial stress. The algorithm is then used to determine the stress and strain fields near the tip of a moving crack in a linear viscoelastic medium. Numerical solutions for both growing and healing cracks are compared with results expected based upon the extended correspondence principle. Excellent agreement between theoretical and numerical solutions is obtained in all cases. Sources of numerical error in the FE solution procedure are identified and documented. The algorithm has not been verified for the non-linear case, since (except for very simple geometries and loading configurations) no closed-form solutions involving non-linear viscoelastic material behaviour are available. A comparison between the measured and predicted response of a non-linear viscoelastic material behaviour will be presented in a following paper.
    Additional Material: 10 Ill.
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