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  • 1970-1974  (148)
  • 1890-1899
  • 1974  (148)
  • 1892
  • Engineering General  (84)
  • Life Sciences  (64)
  • 1
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 45-54 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with a finite element formulation and solution of the boundary value problem of a concentrated force acting on a semi-infinite micropolar solid. A stiffness matrix is derived for a flat micropolar rectangular element in a plane state and use is made of this element to solve the case of the semi-infinite micropolar solid both in a state of plane stress and plane strain. An immediate application of the plane strain case is the important practical problem of a long line load acting on a soil mass which may be simulated as a micropolar body.
    Additional Material: 2 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 111-117 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an extension to the Matrix Transfer Method which gives quadratic convergence to a natural frequency from within a range on either side.The method is described and illustrated by application to: 1A torsional vibration problem, and2A lumped mass beam vibration problem.
    Additional Material: 2 Ill.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 139-165 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation is presented for the equations governing the steady thermohydrodynamic behaviour of liquid lubricated bearings. This formulation permits application of the iterative solution scheme to bearings of arbitrary geometry.A generalized Reynolds equation resulting from the combination of the mass and momentum conservation equations is cast into variational form and used to derive general finite element equations. The method of weighted residuals with Galerkin's criterion is used to generate finite element matrix equations for the thermal energy equation. In addition to the finite element formulation, a discussion of appropriate finite difference techniques is also given for problems without complex geometry.As an example, the formulations are applied to obtain numerical solutions for a three-dimensional sector thrust bearing operating in the thermohydrodynamic regime. Pressure, velocity and temperature distributions are give, and the thermohydrodynamic solutions are compared with the results of classical isothermal theory.
    Additional Material: 11 Ill.
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 203-209 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 215-225 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a general quadratic multilayer plate element is presented for the analysis of arbitrarily layered curved plates. In the formulation, each layer of the multilayer plate can have different orthotropic properties and can deform locally. Examples of bending problems are presented which demonstrate the applicability of the formulation.
    Additional Material: 4 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 249-269 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A structural optimization problem is considered in which the design requirements include restrictions on the strength, stability, frequency and flutter characteristics of the structure. One of the central concerns of this phase of the work has been to overcome the problems inherent in analysing the dynamic and aeroelastic behaviour of structures with many degrees of freedom. The multiweb delta wing structure under supersonic flight conditions is the model upon which this exploratory study is based. The finite element idealization, with three different kinds of elements, is used to model the wing structure. The constant stress triangular plate elements, the rectangular shear panels and the pin-jointed bar elements are used to represent, respectively, the cover skins, webs and stringers of the wing structure. The design problem is formulated as a minimum weight optimization problem and is solved by using non-linear programming techniques. Computationally efficient schemes are developed for the necessary derivatives of the behaviour constraints. Numerical examples are presented to illustrate the feasibility and the computational effectiveness of the method.
    Additional Material: 6 Ill.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 311-321 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 2 Ill.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 209-212 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 214-214 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 277-288 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the stress field due to any prescribed continuous distribution of dislocation dipoles can be determined. This technique then forms the basis of a general method of solution of elasto-plastic material problems. The presentation is limited to situations which conform to either plane stress or strain conditions. Some results are obtained for relatively simple geometrical and loading configurations and compared with classical plasticity solutions. Finally, the method is applied to the problem of a circular hole in a finite strip under tension.
    Additional Material: 10 Ill.
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 295-310 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Through the use of complex series representations and the properties of adjoint differential operators, a semi-analytical finite element procedure is developed which can analyse the steady state and transient temperature fields of thermally anisotropic axisymmetric bodies with complete circumferential properties. Due to its generality, the procedure can handle arbitrary laminate construction with possible meridional and radial variations in locally or globally thermally anisotropic materials. In this respect, the procedure developed herein supercedes the classical semi-analytical treatment which is limited to specially orthotropic materials. Furthermore, in contrast with the classical procedure, the present treatment reveals several important effects of material anisotropy which are entirely missed by the specially orthotropic assumption.
    Additional Material: 10 Ill.
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 395-401 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Physical reasoning makes it possible to use artificial parameters with numerical quadrature in order to obtain approximate solutions for the Fredholm integral equations associated with radiative heat transfer calculations. With the aid of such parameters, decisions can be made concerning the applicability and usefulness of the numerical quadrature technique.
    Additional Material: 6 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 430-431 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 439-440 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 481-494 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element weighted residual process has been used to solve transient linear and non-linear two-dimensional heat conduction problems. Rectangular prisms in a space-time domain were used as the finite elements. The weighting function was equal to the shape function defining the dependent variable approximation. The results are compared in tables with analytical, as well as other numerical data. The finite element method compared favourably with these results. It was found to be stable, convergent to the exact solution, easily programmed, and computationally fast. Finally, the method does not require constant parameters over the entire solution domain.
    Additional Material: 4 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 503-511 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper deals with solving the two-dimensional variational problem for plate bending by the Ritz method using bicubic fundamental splines. It is a piecewise polynomial method, very adaptable to practical numerical computation, and can be an alternative for the well-known Finite Element Method1.
    Additional Material: 3 Ill.
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  • 18
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 821-845 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The visco-plastic model of material behaviour is of much practical interest in its own right and initial strain techniques for its solution have been developed and proved efficient. More important however is the fact that the visco-plastic model can be used to generate plasticity solutions in a simple manner when stationary conditions are reached and, at the other extreme, can reproduce standard creep phenomena. Used in this sense it allows the treatment of non-associated plasticity and strain softening situations which present difficulties in conventional plasticity approaches. A standard programme thus allows the treatment of a wide range of materially non-linear problems.The paper discusses various applications of the new general formulation and introduces certain numerical information on solution stability.
    Additional Material: 12 Ill.
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  • 19
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 803-809 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The elastoplastic deformation of spherical shells of uniform thickness acted upon by external pressure is investigated in this paper. A deformation theory of plasticity is combined with the classical elasticity equations and a solution is obtained by the method of successive elastic solutions. A logarithmic effective stress-effective plastic strain diagram is used to determine the volume change for thick polypropylene spheres under the action of external pressure. These results are compared with previously published experimental volume changes in polypropylene spheres. This comparison shows that the predicted volume changes are similar to the experimental results.
    Additional Material: 1 Ill.
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  • 20
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 913-914 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 21
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 917-918 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 22
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 212-212 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 271-276 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fitting of a function y =\documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} to experimental data is considered. Integral equations are developed which have the functions \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\nolimits_{i = 1}^n {A_i {\rm{e}}^{\lambda ix}} $\end{document} as their solutions for n = 1, 2, 3, These integral equations are used to find the frequencies λi. Examples are worked out to illustrate the method. The method is shown to be capable of extension to other functions.
    Additional Material: 2 Tab.
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  • 24
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 289-294 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To obtain meshes of reasonable form there have to be made some restrictions in the application of automatic mesh generation schemes using ‘isoparametric’ co-ordinates. In this present paper it will be shown that such restrictions exist for plane meshes. The results figured here are also valid for three-dimensional meshes.
    Additional Material: 4 Ill.
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  • 25
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 341-358 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A least square based finite element algorithm is developed for some elasto-static problems. In the formulation both stresses and displacements appear as simultaneous variables. In two dimensional (plane) analysis, parabolie isoparametric elements are used. Considerable improvement of performance is obtained with a numerical integration based on 2 × 2 Gauss point distribution over more accurate integration schemes. Reasons for this are presented.The formulation is extended in the section ‘General least square formulation’ to beams and plates with a similar success of ‘reduced’ integration.
    Additional Material: 11 Ill.
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  • 26
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 323-339 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite strip method is presented for determining the initial buckling stresses of any structure consisting of a series of thin flat isotropic plates rigidly connected together at their longitudinal edges. Each plate may be subjected to a combination of longitudinal and transverse compression, longitudinal in-plane bending, and shear, and it is assumed that the buckling mode, of whatever type, is sinusoidal in the longitudinal direction. Due to the presence of shear, the perturbation forces and displacements which occur at the edges of component plates during buckling are out of phase, and this is accounted for by defining their magnitudes in terms of complex quantities. Stiffness matrices relating the amplitudes of these forces and displacements are derived using an approximate method based upon assumed displacement functions across the width of the plate. It is shown how the method can be used to calculate natural frequencies of prismatic structures, and finally an indication of the accuracy of the method is given together with some illustrative results.
    Additional Material: 8 Ill.
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  • 27
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    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 403-414 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By representing the time-dependent material properties by mechanical models, i.e. the generalized Maxwell and/or Voigt (or Kelvin) models, it is possible to formulate a consistent procedure to analyse the effect of material damping on dynamic response. As a continuation of the previous work which concerned the creep and relaxation of viscoelastic materials, the present paper applies this representation to the harmonic response analysis. The harmonic solution can be obtained by decomposing the relevant forces and displacements into real and imaginary parts and it is shown that the modal analysis by an appropriate eigensolution procedure is useful for obtaining the dependence of vibration amplitude on frequencies of sinusoidal external excitations.
    Additional Material: 6 Ill.
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  • 28
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 513-519 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Edge displacement of assumed-stress hybrid plate elements are commonly chosen as either linear, quadratic or cubic functions of the edge co-ordinate. The present paper examines the effect of this choice on the acceptability, accuracy, and possible zero energy modes of elements based on a linear stress field. It is concluded that triangular elements may be preferable to quadrilaterals, and that linear edge displacements are not desirable.
    Additional Material: 5 Ill.
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  • 29
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 537-545 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a generalized quadrilateral finite element that includes a singular point at a corner node is presented. Inter-element conformability is maintained so that monotone convergence is preserved. The global-local concept of finite elements is used to formulate the complete set of equations. Examples of crack tip singularities are given.
    Additional Material: 6 Ill.
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  • 30
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 547-567 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The triangular element is one of the most useful finite difference elements for the potential problems because of its versatility in fitting irregular boundary, in connecting one element type to another, and in changing grid fineness. Such triangular elements find many applications in conduction problems in cartesian co-ordinates. This paper presents a new triangular element for the finite' difference solution of axisymmetric conduction problems in cylindrical co-ordinates. The validity of the proposed triangular element is analyzed, and its workability is demonstrated using three selected examples. Also, an industrial application highlights the advantageous characteristics of the triangular element, and gives a comparison with known results obtained by finite element method.
    Additional Material: 10 Ill.
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  • 31
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 569-588 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Basic equations are derived for a comprehensive computer analysis for an equivalent lumped parameter system which simulates a pre-twisted, rotating or non-rotating. Timoshenko beam in coupled bending-bending-torsion vibrations. These equations enable one to develop straightforwardly digital computer programs for studying vibration problems related to compressor or turbine blades in turbomachinery as well as in other structural dynamics applications. The validity of the lumped parameter approach is established through a free vibration study. Good agreement between the present computer results and those obtained theoretically or experimentally by other investigators is demonstrated. In particular, it is found that the natural frequencies obtained in the free vibration study for all beams examined converge from below the exact values at a convergence rate of N-4, where N is the total number of the lumped parameters used in the computer simulation. The rapid rate of convergence shows that the mathematical model used in deriving the basic equations can adequately represent the type of beams under consideration. The known convergence rate also provides an estimate on the accuracy of the computer results, and a means to improve these results by extrapolation.
    Additional Material: 6 Ill.
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  • 32
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 659-661 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 1 Tab.
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  • 33
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 662-670 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A unified procedure is presented for the automatic generation of the coefficient matrix of finite difference equations. The method is applicable to the solution of both initial and boundary value problems, to any order of difference equation, and may be used with any arbitrary initial or boundary conditions.
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  • 34
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 671-675 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method of determining the torsional stiffness of a wide range of structural sections, both homogeneous and composite, is presented. Prandtl's stress function along the boundaries of component sections is approximated by finite Fourier series with coefficients chosen to minimize a functional. An example indicates that the stiffness may be determined to acceptable accuracy by the solution of very few equations.
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  • 35
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 697-711 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is shown how the elasticity equations can be formulated in terms of a general procedure of abstract analysis, called the projective method, for constructing an approximate solution. This allows the many studies of convergence and uniqueness of solutions which have been made in modern mathematics to be applied to the elasticity problem. The abstract formulation also suggests an organizational scheme for generating a computer code. A computer code for hollow or solid cylinders of arbitrary cross section was developed and several numerical examples are presented. The procedure is computationally advantageous for the class of problems under consideration because of the relatively small number of equations that must be solved as compared to the finite element method. The results presented demonstrate the accuracy of the method.
    Additional Material: 9 Ill.
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  • 36
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 37
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 743-770 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The discrete (Legendre) orthogonal polynomials, (DLOP's) are useful for approximation purposes. This set of mth degree polynomials {Pm(K, N)} are orthogonal with unity weight over a uniform discrete interval and are completely determined by the normalization Pm(O, N) = 1. The authors are employing these polynomials as assumed modes in engineering applications of weighted residual methods. Since extensive material on these discrete orthogonal polynomials, and their properties, is not readily available, this paper is designed to unify and summarize the presently available information on the DLOP's and related polynomials. In so doing, many new properties have been derived. These properties, along with sketches of their derivation, are included. Also presented are a representation of the DLOP's as a product of vectors and matrices, and an efficient computational scheme for generating these polynomials.
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  • 38
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    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 783-801 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The patch test is shown to be contained in the variational formulations of the finite element methods at the assembling level, all of which require the vanishing of the virtual work of interface connection loads. By a systematic introduction of stress generating functions, attention is drawn to the fact that any given finite element model can be assembled in two different ways: either by identification of a set of boundary displacements (leading to the direct stiffness method), or by identification of a set of local stress function values (leading to the dual direct flexibility method). Looking at any conjugate couple (generalized displacement-generalized surface traction) at an interface, one is strongly transmitted, the other weakly. Discretization of the zero virtual work condition at an interface of plate bending models, by means of Legendre polynomial expansions, allows a systematic construction of so-called ‘non-conforming’ elements that pass the patch test. They are in fact identified with weakly conforming, but strongly diffusive, hybrids, and the lowest degree element (quadratic) is in fact the Morley constant-moment element. Examples are given for higher degree displacement fields.The case of plate stretching elements can be handled by duality, the difficulties being here associated with the requirements for diffusivity. Non-diffusive elements that pass the zero interface virtual work test can be constructed systematically and are identifiable with weakly diffusive, but strongly conforming, hybrids of the type first proposed by T. H. H. Pian.
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  • 39
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    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 40
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 27-43 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Body oriented co-ordinates are defined for three-dimensional regions bounded by six surfaces. From this definition of body oriented co-ordinates, two transformations are derived: 1Body oriented surface co-ordinates to the Cartesian co-ordinates, and2Body oriented co-ordinates for a three-dimensional region to Cartesian co-ordinates.With these transformations a mesh generator is developed based on the principle that the mesh required to describe a region will be calculated according to the placement of the discrete points that describe the boundary edges. This is accomplished with two versions of the mesh generator: the surface generator and the volume generator. The surface generator maps the four boundaries of the surface onto the four boundaries of a unit square. Next, the interior points for the surface mesh are established in the mapped space. Then, using the first transformation, the co-ordinates for the surface nodal points are calculated. Similarly, the volume generator maps the six surfaces of the body onto the surfaces of a unit cube, establishes the interior nodal points in the mapped space, and using the second transformation, calculates the co-ordinates for the interior nodal points.
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  • 41
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 359-367 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes a method of solving electromagnetic induction problems by means of the finite element technique. A variational equation associated with the differential equation for the vector potential is formulated and solved via the concept of finite elements. Sinusoidal driving currents and linear, isotropic, but inhomogeneous media are assumed. A typical example is included in order to illustrate the suggested solution technique.
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  • 42
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 369-394 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The mesh generation program described here generates the nodes and the elements for excavated highway slopes, applies boundary conditions, searches for the nodes and the elements in each layer excavated and plots the mesh with the numbering of nodes, elements and material types.
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  • 43
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 415-424 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element analysis applicable to elasto-plastic shells of arbitrary shape is presented. Small-deflection behaviour of thin shells subjected to monotonically increasing static loads is considered. The material is assumed to be originally isotropic, following the von Mises yield criterion and the Prandtl-Reuss flow rule. A flat triangular element with twelve degrees of freedom is used in the analysis. Within each element both membrane forces and bending moments are assumed to be constant. Some numerical results are included to illustrate the merits of the element.
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  • 44
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 425-429 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A procedure to deal with various boundary conditions in the Rayleigh-Ritz method is discussed herein, namely, the method of artificial parameters. The method is then applied to solve a simple string problem; results obtained compare very nicely with exact solutions.
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  • 45
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 431-432 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 46
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 433-437 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: One of the first finite elements presented was that by Turner et al.1 Pian2 presented a hybrid plane stress element and Wilson et al.3 presented a non-conforming displacement element. It is shown that the three resulting stiffness matrices are identical.
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  • 47
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 461-480 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The concepts and potential advantages of local and global least squares smoothing of discontinuous finite element functions are introduced.The relationship between local smoothing and the ‘reduced’ integration' technique is established.Examples are presented to illustrate the application of the two smoothing techniques to the finite element stresses from several structural analysis problems.The paper concludes with some practical recommendations for discontinuous finite element function smoothing.
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  • 48
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 495-501 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a two-dimensional space of points on an equilateral triangle grid, a single difference equation holding at each node is found from the finite element formulation of the wave equation for all published polynomial orders of the functional expansion. Assuming homogeneous boundary conditions on any equilateral triangle whose edges and vertices pass through the grid points, the eigensolutions of the difference equation are found exactly and thus provide an excellent test problem for the programmer or engineer. The advantage of the present method over other formulations is that the number of linear operations required to produce the difference equation is minimal.
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  • 49
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 429-430 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 50
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 432-432 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 51
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 438-438 
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  • 52
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 443-460 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A number of problems are analysed by the displacement method to assess the stress accuracy at very low compressibilities. ‘Parabolic’ isoparametric elements are used. It is found that the mean stress becomes grossly in error at the centre and edges of each element as the compressibility is reduced whereas the deviatoric stress components do not. All stress components retain good accuracy at the ‘reduced’ integration sampling points (2 × 2 Gauss). ‘Exact’ integration yields a similar stress distribution to ‘reduced’ but the mean stress is grossly in error at the integration points (3 × 3 Gauss). Exceptions, however, occur.These findings are interpreted, and a rule for predetermining whether or not accurate stresses can be obtained at the integrating points is suggested. Thus it is shown that the displacement method is suitable for analysing materials which for practical purposes are incompressible.A procedure is then presented for analysing porous media-both linear and non-linear-by separating the stiffness into ‘effective’ and ‘pore fluid’ components. This allows excess pore pressure to be calculated explicitly. Applications to saturated soils are given which make use of the findings of the first part of the paper.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 529-536 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The steady state flow problem known in magnetohydrodynamics as Hartmann's flow is converted into variational formulation and is given an approximate solution by means of the spline blended interpolation technique. The equations of motion consist of two coupled potential flow problems with homogeneous boundary conditions. The spline blended interpolation method is reduced here, because of the shape of the domain, to a cartesian product of cardinal splines with trigonometric or ordinary polynomials. ‘Exact’ boundary conditions are presented by the blending technique. The numerical results indicate that high accuracy is possible with relatively few unknowns.
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  • 54
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 613-624 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper presents a generally applicable approach to transient heat conduction problems with non-linear physical properties and boundary conditions. An unconditionally stable central algorithm is used which does not require iteration.Several examples involving phase change (where latent heat effects are incorporated as heat capacity variations) and non-linear radiation boundary conditions are given which show very good accuracy.Simple triangular elements are used throughout but the formulation is generally valid and not restricted to any single type of element.
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  • 55
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 625-631 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A program is demonstrated which apart from linear finite elements in time also includes elements with shape functions of the second and third degree. The algorithm for discretization in the time dimension is described and, using the example of a parabolic time element, the coefficients required to form the global system are given. By various test examples the efficiency of the process is examined by comparison with the customary difference method. Generally, with finite elements in time, the solution has better stability. Comparing the time required for calculation with the accuracy of the solution it would appear that in examining problems where boundary conditions are constant in time, higher order time elements are no improvement over the linear time element. However, for the purpose of reproducing periodic processes, higher order time elements offer an advantage in that one is not limited to linear variations of the boundary conditions within the element. Thus, for example, the temperature curve for parabolic variation of the surface temperature can be reproduced with close approximation by two time elements per period and a shape function of the third degree.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 676-676 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 57
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 771-781 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The steady two-dimensional, viscous, electrically conducting flow around a circular cylinder is investigated. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The equations and boundary conditions are derived for arbitrary values of R, Rmand β, where R is the Reynolds number, Rm the magnetic Reynolds number and β, the ratio of the square of the Alfvén speed to the square of the main stream speed. Because of the large number of parameters involved, the numerical solution is restricted to R = 40, Rm = 1 and infinity and 0 ≤ β ≤ 4. Also the cylinder is taken to be a perfect conductor, this avoids having to compute the magnetic field within the cylinder.The numerical computations for the non-magnetic case, i.e. β = 0, are presented and are found to be in good agreement with existing results. The effect of increasing the strength of the magnetic field (i.e. increasing β) on the drag coefficient, the size and position of the standing vortex and the increasing effect of the upstream propagation of disturbances are examined.
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  • 58
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 811-820 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We describe a finite element method for the one-dimensional Stefan problem. The elements are quadrilaterals of the space-time plane which are determined at each time-step in relation with the position of the free boundary. The method appears as a generalization of the classical Crank-Nicolson scheme, since it is identical to this scheme in the case of rectangular elements; it has the advantage of providing a simple and accurate determination of the free boundary. Numerical experiments show that the order of accuracy is equal to 2.
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  • 59
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 865-876 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Based on the least squares error criterion, a class of finite element is formulated for the numerical analysis of steady state viscous boundary layer flow problems. The method is essentially a discrete element-wise minimization of square and weighted residuals which arise from the attempts in approximately satisfying boundary layer equations. An iterative linearization scheme is developed to circumvent the mathematical difficulties posed by the non-linear boundary layer equations. It results in a process of successive least squares minimizations of residual errors arising from satisfying a set of linear differential equations. A mathematical justification for the method is presented. A major feature of the method lies in the linearization approach which renders non-linear differential equations amenable to linear least squares finite element analysis. Another important feature rests on the proposed finite element formulation which preserves the symmetric nature of finite element matrix equations through the use of the least squares error criterion. Numerical examples of viscous flow along a flat plate are presented to demonstrate the applicability of the method as well as to illuminate discussions on the theoretical aspects of the method.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 917-917 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 61
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 847-864 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite beam-column element computer program for the structural failure analysis of proportionally loaded skeletal plane frames is described. The program, which is based on an iterative stiffness approach, provides for non-linear elastic or plastic-non-linear elastic behaviour. Particular attention is given to the incorporation into the analysis of geometrical imperfections, return of elasticity at plastic hinges and negative frame stiffness. The effect of lack-of-fit displacements on the load-deflection path and failure load of frames that carry relatively large axial loads is described in general terms. The theory is developed further through the application of the computer program to two examples which show the necessity for the allowing for the effect of imperfections when designing axially loaded redundant frames.
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  • 62
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    Notes: This article presents an efficient numerical algorithm a complete listing of the associated computer program, developed for the eigenproblem solution of discrete damped structures, including spinning ones. The numerically stable procedure is based on a combined Sturm sequence and inverse iteration technique, which fully exploits the banded form of the relevant matrices and proves to be most substantially economical when compared to similar existing softwares. Numerical results are presented for representative structures, solved by the present computer program written in FORTRAN V for the JPL UNIVAC 1108 computer.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 17-25 
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    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three variational statements for the slow time-independent flow of a Navier-Poisson fluid are derived. All of these statements are suitable as the bases of finite elements. The first statement is applied successfully to several flow situations.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 91-102 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper deals with the numerical solution of wave propagation problems in general although the primary area of interest is elastodynamics. The work is applicable to a variety of wave propagation phenomena of classical physics. Explicit schemes of Strang type are used, which allow many simplifications over existing methods. The Strang schemes allow in a very real but perhaps unexpected way the splitting of the elasticity operator.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 71-90 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: By use of the least squares error criterion, an alternate finite element formulation is presented. The method is based on the discrete or element-wise minimization of square and weighted differential equation residuals which are expressed in terms of element nodal quantities. In order to overcome the stringent inter-element continuity requirement, a major stumbling block, on the element trial functions two practical schemes are proposed. One is the reduction of the original governing differential equation to a system of equivalent first order differential equations; the other is a method of smoothing discontinous trial functions. The latter essentially relaxes the continuity requirement and yields efficient non-conforming finite elements. This paper also demonstrates the use of constant weights which significantly improves the rates of convergence. Several numerical examples illustrate the proposed method. From these examples, it may be concluded that the use of constant weights and the relaxation of the inter-element continuity requirement are two indispensable features of the weighted discrete least square method.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 119-138 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A direct method is described for the evaluation of the critical loads on deep circular arches having various forms of end support. The method is applicable to arches of non-uniform flexural rigidity and may cater for arbitrary forms of applied load distribution. The results calculated for two examples are given, and compared with those obtained analytically and experimentally by other investigators. A complete listing of a computer program for one of the examples is provided in the Appendices.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 195-198 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element method for the analysis of axisymmetric bodies in torsion is presented. The effects of an angular acceleration about the axis of symmetry is included. The accuracy of the method is tested against experimental results available for a stepped shaft and finally the problem of an accelerating shaft-turbine disc system is considered.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 1-16 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: When large, progressive, deformation occurs under plastic or visco-plastic conditions, elastic deformations are negligible and the material flows in a viscous manner. The flow is non-Newtonian and the viscosity is a function of the current strain rates. An effective numerical treatment of such non-Newtonian flow by the finite element method is indicated here and is illustrated by examples of an extrusion process for which approximate slip line solutions are known.The methodology is extended to the solution of transient, quasi-static situations and coupling with thermodynamic equations is discussed.A stream function formulation of the problem is used.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 55-69 
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    Notes: The finite element method is applied to dynamic linear viscoelastic analysis. The arising system of differential equations is integrated by means of the Laplace transformation. The direct numerical evaluation of the inversion integral seems to be appropriate in case of vibrational problems. The method is applied to examples of transient vibrations of elastic bodies. Initial conditions and arbitrary damping matrices can be considered.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 103-110 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper discusses three numerical integration schemes connected with a finite element solution to the transient heat-conduction equation. The main emphasis is on the achievable accuracy. A simple recurrence relation derived from the Galerkin process is suggested for the treatment of fast-varying boundary conditions as being significantly better than the usual Crank-Nicholson scheme in matters of short-time accuracy.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 167-194 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Use of mixed force and displacement variables may be the key to a reliable solution of many physical problems. For the analysis of elastic structures with large rigid motion the displacement method may fail due to illconditioning, but use of mixed variables (diacoptics) may work due to the possibility of using relative displacements within substructures. Analysis with mixed variables complicates the topology (the number of nodes and the number of variables at the nodes may vary in the same problem) so a careful study of the system analysis is required. Some general computer routines are given for handling topology, merging and solution of the sparse system equation. The solution routine handles constraints in a rational way and can also be used for decomposition of the system equation or for releasing inner nodes in superelements.
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 198-203 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the static condensation method is discussed in general. The technique is presented as an extension of the Gauss elimination algorithm. An efficient FORTRAN subroutine is given which simultaneously reduces both the stiffness matrix and the stress-displacement transformation matrix.
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  • 73
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 212-212 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 74
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    International Journal for Numerical Methods in Engineering 8 (1974) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 75
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 227-248 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integrated sequential computer programme for the solution of large linear algebraic systems encountered in the discrete analysis of complex structures using finite element idealization is described. The programme uses an algorithm based on Gauss elimination for solution and is independent of the possible symmetric nature of the system matrix thus enhancing the applicability of the programme for systems with unsymmetric coefficient matrices. The present programme can handle large band widths and the core memory is used efficiently for all feasible problem sizes. A FORTRAN print-out of the programme with relevant explanatory comments and a full notation list are appended.
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  • 76
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 521-528 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two methods are presented for the automatic selection of a cycle basis leading to a sparse flexibility matrix for the analysis of rigid-jointed skeletal structures.The first method having a local approach forms a maximal set of admissible minimal cycles, while the second having a global approach constructs admissible minimal cycles on the ordered chords of a shortest route tree. A cycle ordering algorithm is also given to reduce the band width of the corresponding flexibility matrix.
    Additional Material: 3 Ill.
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  • 77
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 589-611 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a method of solving systems of simultaneous non-linear partial differential equations using the method of lines and the method of quasilinearization-superposition in combination. The advantages of the method over those methods more generally used are discussed and an example of the application of the method to the two-dimensional momentum and energy equations considering temperature-dependent and/or shear-rate dependent viscosity is given.
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  • 78
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 649-657 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
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  • 79
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 633-647 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of ‘least squares’, which falls under the category of weighted residual processes, is applied as a time-stepping algorithm to one-dimensional transient problems including the heat conduction equation, diffusion-convection equation, and a non-linear unsaturated flow equation. Comparison is made with other time-stepping algorithms, and the least squares method is seen to offer definite advantages.
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  • 80
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 676-676 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 81
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 679-696 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The object of this paper is to describe a new algorithm for the semi-automatic triangulation of arbitrary, multiply connected planar domains. The strategy is based upon a modification of a finite element mesh genration algorithm recently developed. 1 The scheme is designed for maximum flexibility and is capable of generating meshes of triangular elements for the decomposition of virtually any multiply connected planar domain. Moreover, the desired density of elements in various regions of the problem domain is specified by the user, thus allowing him to obtain a mesh decomposition appropriate to the physical loading and/or boundary conditions of the particular problem at hand. Several examples are presented to illustrate the applicability of the algorithm. An extension of the algorithm to the triangulation of shell structures is indicated.
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  • 82
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 731-741 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A polynomial shape function of triangular elements for finite element analysis of general deformation of sheet metals with or without orthotropic anisotropy is proposed. And general formulation for large deformation and large strain analysis with non-linearity of material property, say plasticity, is given. Some numerical examples are examined with respect to hydraulic bulging.
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  • 83
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 713-729 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A characteristic feature of the variational functionals for several boundary value problems in polar co-ordinates is the fact that one independent variable occurs explicitly in the denominator. Therefore, the coefficients of the finite element equations for sectors of circular ring shaped elements are not constants but functions of the distance of the elements from the origin of co-ordinates.1 We name them coefficient functions. In order to show the particular aspects of the calculations in terms of polar co-ordinates we deal here with the solution of the torsion problem by bilinear and bicubic Hermitian interpolation.The finite element equations are arranged according to Schaefer2 in the form of block which can easily be transformed into ‘stars’3 or molecules4,5 similar to those used in finite difference methods. The origin of co-ordinates requires a special consideration, firstly because of the coincidence of several nodes at that point and secondly because of the divergent behaviour of some coefficient functions. It turns out to be advantageous for the numerical calculations to expand the coefficient functions in power series. Besides, the expansions are required to deduce the equations for rectangular elements by limiting processes. The twisting moments and shearing stresses calculated for several cross sections illustrate the numerical suitability of the method. The finite element values are compared partly with exact solutions and partly with experimental results obtained by a moiré method using Prandtl's soap film analogy.6 Finally it is shown how the accuracy of the finite element values can be improved by the Richardson extrapolation7.
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  • 84
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    International Journal for Numerical Methods in Engineering 8 (1974), S. 914-916 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper shows a procedure for estimating the shape parameter of a Gamma distribution from a sample. This procedure uses a rapidly converging iteration to solve the maximum-likelihood equation and suggests a simple formula for determing the starting value.
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  • 85
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: The antibiotic chlorotetracycline (CTC) is used as a fluorescent chelate probe to investigate its active transport in respiring Staphylococcus aureus cells. CTC chelation to magnesium or calcium leads to fluorescence enhancement. This enhancement is further increased when the polarity of its environment is decreased, as occurs when the complex moves from an aqueous environment into a membrane. Upon addition of CTC to a dispersion of S. aureus cells, a time dependent fluorescence enhancement is detected which is a monitor of the transport of the CTC-divalent cation complex into the membrane. This uptake has been shown to be energy dependent and exhibits saturation kinetics with an apparent Km of 107 ± 20 μM by the same technique. The initial rates of antibiotic uptake are shown to have a pH optimum between 5.5 and 6.5. The effects of exogenously added EDTA and paramagnetic Mn2+ indicate that the CTC-divalent cation complex is transported to the inside of the membrane. Exogenously added magnesium inhibits the accumulation process. This implies that the membrane CTC binding site involves a divalent cation sequestered away from the surface of the membrane, and only free CTC is bound to that site. The uptake of CTC is also temperature dependent with a maximal rate at 40°. Arrhenius plots of the initial fluorescence enhancement rates are found to be biphasic with a 27° transition temperature. The break in the plots presumably reflects an order-disorder transition involving the fatty acids of the cell membrane. Thus, transport of the CTC involves movement through the fatty acid region of the membrane. This movement is facilitated by the more fluid state of the membrane above the transition temperature.
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  • 86
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    Journal of Supramolecular Structure 2 (1974) 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
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  • 87
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    Journal of Supramolecular Structure 2 (1974), S. 349-359 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: groE bacterial mutants of E. coli have been isolated on the basis of their inability to propagate bacteriophage λ. The block exerted on λ growth has been shown to operate at the level of head assembly. Some groE mutations express pleiotropic effects, such as inability to propagate T4 and T5 or inability to form colonies at high temperature. P1 transduction experiments show that these groE mutations map at 83 min on the genetic map of E. coli and that a single mutation is responsible for the pleiotropic effects observed. At 43°C, some of the groE strains are temperature sensitive for growth and form long filamentous structures. Examination of the proteins synthesized at 43° by one of the temperature-sensitive groE strains, groEA44, by SDS gel electrophoresis reveals a pattern of synthesis somewhat different from that exhibited by the gro+ parent strain: some new bands appear, while others disappear.
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  • 88
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    Journal of Supramolecular Structure 2 (1974), S. 337-348 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Satellite phage P4 causes the head proteins of a helper phage, such as P2, to form a small head. This small head is never found in cells infected by the helper virus alone. This finding, coupled with the dominance of P4 over its helper, indicates that the P4 genome has the potential for specific head size determination. Satellite phage P4 codes for a late protein which is found in the P4 head (45 copies/head). This protein may determine head size. Our finding that the small size of P4 DNA does not determine small head size in an in vitro DNA packaging system lends further support to the idea that a P4 protein determines small head size.Formation of P2 headlike structures is accompanied by cleavage of P2 head proteins. Cleavage of the major head protein precursor can be observed in vitro after lysis of infected cells with lysozyme. The rate of this in vitro reaction is not affected by deoxyribonuclease; thus there cannot be a tight coupling between DNA packaging and the cleavage of the major capsid protein.
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  • 89
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    Journal of Supramolecular Structure 2 (1974), S. 582-592 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: The acetylcholine receptor from Torpedo californica electroplax has been studied at three levels of molecular organization: receptor-rich membrane fragments, solubilized and purified receptor, and reconstituted receptor in phospholipid vesicles. The binding of cholinergic ligands to the membrane-bound and the solubilized material is not cooperative, and the number of ligand sites is less than the number of toxin sites. In addition, the purified macromolecule contains the molecular features necessary for ion-translocation during postsynaptic depolarization, since a chemically excitable membrane can be formed from purified receptor and Torpedo phospholipids.
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  • 90
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    Journal of Supramolecular Structure 2 (1974), S. 609-616 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Lateral phase separations in lipid and lipid-protein systems are discussed with the aid of phase diagrams derived from spin-label measurements. Freeze-fracture data from E. coli membranes and model lipid-protein bilayers indicate that the protein tends to associate with fluid lipid phases.
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  • 91
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    Journal of Supramolecular Structure 2 (1974), S. 646-669 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Presently there is much interest in the relationship between the structure and function of biological membranes. An approach to the understanding of this relationship has been the study of the effect of the modification of the membrane lipids on the function of membrane-associated activities. In our laboratories we have modified the apolar portion of the membrane lipids of unsaturated fatty-acid auxotrophs of Escherichia coli and investigated the effect of such modifications on enzymes of the electron-transport system. From these studies we were able to conclude that E. coli regulates the relative fatty-acid content of its phospholipids and maintains a certain membrane fluidity necessary for proper membrane function (1-3). We have also proposed that lipids are heterogeneously distributed within the membrane in domains of differing fluidity (4). The studies of McConnell, Chapman, and others (5-13) have corroborated these concepts and extended them to other biological and model membranes. In this paper we review some of our previous results and present evidence to show how NADH and D-lactate oxidases of E. coli membranes are influenced by the fluid states of membrane phospholipids. Preliminary evidence is also presented to show that biogenesis of membranes probably occurs by independent insertion into the membranes of lipids and proteins which upon subsequent interaction with each other form the functional lipoprotein units.
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  • 92
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    Journal of Supramolecular Structure 2 (1974), S. 670-681 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Detergent-solubilized proteins and lipids of mycoplasma membranes reassemble spontaneously into membranous structures on the removal or dilution of the detergent in the presence of divalent cations. The cations seem to function by neutralizing the negatively charged groups on membrane lipids and proteins which interfere by electrostatic repulsion with membrane reassembly. Moreover, salt bridges formed by the divalent cation between acidic groups on membrane proteins and lipids seem to play an important role in the reconstituted membrane stability. Electron transport activity, as measured by the transport of electrons from NADH to oxygen, has been demonstrated in reconstituted Acholeplasma laidlawii membranes. However, restoration of active transport of sugars or ions has not been achieved so far. The conditions for obtaining properly sealed vesicles, which are obligatory for demonstrating transport activity, are still rather poorly defined. The reassembled membranous structures cannot be distinguished from the native membranes in chemical composition, density, and thin sections. However, probe techniques, x-ray diffraction, and freeze-fracturing electron microscopy indicate that the proteins are organized differently in the reassembled membranes, though the lipid bilayer is restored. The results obtained so far leave little hope for successfully reconstituting the molecular organization of membranes as complex as those of mycoplasmas by a single-step reassembly of detergent-solubilized membrane components. The prospects appear brighter with membranes having only a few protein species, such as the outer membrane of gram-negative bacteria. In spite of the failure to reconstitute fully active mycoplasma membranes, the reassembly procedure was found valuable in studying the interactions of detergent-solubilized membrane proteins with lipids, the effects of a hydrophobic environment on hydrophilic enzymes, and the production of “hybrid” membranes having selected membrane components.
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  • 93
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    Journal of Supramolecular Structure 2 (1974), S. 150-162 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: We have purified actin and my osin-like proteins from amoebae of Dictyostelium discoideum. These proteins are very similar in their physical and enzymatic properties to muscle actin and myosin. Most importantly, they form thin and thick filaments, respectively, and Dictyostelium actin activates Dictyostelium myosin ATPase activity. Actin from these amoebae appears to be identical in size to muscle actin. The Dictyostelium myosin consists of two heavy chains of about 210,000 daltons and two classes of light chains, about 18,000 and 16,000 daltons. The heavy chains are slightly larger than those of muscle myosin. Biochemical and structural studies of membrane association of the contractile complex suggests that some of the amoeba actin is membrane-bound and acts as an attachment point for myosin and other actin filaments.
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  • 94
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    Journal of Supramolecular Structure 2 (1974), S. 202-224 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: About 250 molecules of the 42,000 molecular weight gene 8 product catalyze the polymerization of the major phage coat protein into a precursor shell temporarily containing both proteins. The resulting prohead appears to be a shell structure with the P8, or scaffolding protein, on the inside, and the coat protein on the outside. In concert with DNA condensation inside the shell, all 250 scaffolding molecules exit from the prohead, without proteolytic cleavage. These molecules then recycle and catalyze the formation of more proheads from newly synthesized coat protein. Such proteins, which catalyze assembly by temporarily associating with an intermediate stage, may represent a general mechanism of macromolecular assembly.
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  • 95
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    Journal of Supramolecular Structure 2 (1974), S. 429-450 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Microtubule polymerization in vitro was examined using material purified from porcine brain tissue by a reversible temperature dependent assembly procedure, and was characterized by electron microscopy, viscometry, and sedimentation. The reaction was endothermic, colchicine sensitive, and occurred at neutral pH and moderate ionic strength. Divalent cations (calcium, magnesium) were inhibitory at millimolar concentrations, but stimulated polymerization at the micromolar level. Nucleoside triphosphates were required for assembly of purified subunits. As determined by quantitative sedimentation analyses, the reaction was an equilibrium process. Below a critical concentration of tubulin no assembly occurred. Analytical ultracentrifugation studies indicated that tubulin species with sO20, w of 6S and 30S were in equilibrium with each other, and that both were incorporated into microtubules. Electron microscopic analyses suggested that disc (or ring) structures might be intermediates in assembly, and that they were primarily utilized early in the polymerization process. Assembly could be seeded by mixing microtubular fragments from brain or flagella with brain microtubule subunits; depending on conditions of temperature and protein concentration, addition of subunits occurred either with unipolar or biased polar directionality. The possible significance of these properties of the polymerization reaction for control of assembly is discussed.
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  • 96
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    Journal of Supramolecular Structure 2 (1974), S. 451-465 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Beef brain tubulin isolated by cycles of polymerization and depolymerization contains two components, 6S subunit and a 25-35S boundary containing ring-shaped aggregates of tubulin. The rings disappear during microtubule polymerization, and the incorporation of ring tubulin into microtubules has been investigated by studying the changes in the sedimentation of tubulin which occur during polymerization. The “30S” boundary was separated from the 6S boundary by sedimentation at low temperatures. The temperature was then raised by letting a small amount of air into the vacuum chamber and the changes in sedimentation rate and concentration of each component determined as the tubulin polymerized. The 30S material polymerizes preferentially as determined by its decrease in concentration at polymerizing temperatures. Simultaneously with its decrease in concentration the 30S also decreases in sedimentation rate. The decrease in concentration of the 30S correlates well with polymerization while the decrease in sedimentation rate can occur independently of polymerization. The results indicate that the rings are not transformed directly into microtubules, but break down into subunits or small aggregates and these then assemble into microtubules. The rings may serve as a “storage aggregate” of active subunits. The presence of a possible storage aggregate in a dividing cell, the eggs of the surf clam, Spisula solidissima, has been indicated by measurements of particulate tubulin changes during the cell cycle. Microtubule assembly in vitro in homogenates of these eggs indicates that the amount of tubulin which forms microtubules may be controlled by the functioning of the microtubule organizing center.
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  • 97
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    Journal of Supramolecular Structure 2 (1974), S. 512-514 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: The status of research on macromolecular assembly is similar in several respects to that of research on macromolecular synthesis in the late 1950's. The work of that era can teach us some lessons, but it also has left us with some preconceptions that may be misleading us in our attempts to understand assembly mechanisms.
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  • 98
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    Journal of Supramolecular Structure 2 (1974), S. 538-557 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Alamethicin, monazomycin, or EIM induce electrical excitability in lipid bilayers. The voltage-dependent gating displays all the characteristics observed in excitable cells and its basic features can be quantitatively described by the Hodgkin-Huxley equations.A common molecular mechanism of membrane excitation has been postulated. It assumes that in the absence of an electrical field the channel-forming molecules lie at the surface of the membrane. An applied potential tilts them from the surface into the hydrocarbon region of the bilayer. Once in this position the molecules diffuse laterally and form aggregates which act as channels for the flow of ions.In the case of alamethicin we assume that the molecule forms an elongated ellipsoid with two glutamic residues at one end, and a metal ion in four- or five-fold coordination with peptide carbonyl oxygens at the other. An applied field pulls the cationic end through the membrane to the other side, while the glutamic residues hold the other end attached to the original surface. The molecules now span the membrane and aggregate, forming oligomeric channels in which most of the peptide carbonyls face toward the center, and the methyl groups outward.Monomers and dimers do not conduct and an individual channel can have different conductance values depending on the number of monomers in the aggregate and the resulting channel diameter. A quantitative description of this process matches observed gating kinetics, gating currents, and the single channel conductance increments. Without additional assumptions, inactivation follows directly from the aggregation process because with proper rate constants, the average degree of polymerization and therefore number of open channels goes through a maximum in time.The model may also apply to the excitation process of higher cells.
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  • 99
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    Journal of Supramolecular Structure 2 (1974), S. 558-581 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Internal dialysis techniques have been used to examine the influence of external and internal cations on Ca efflux from ATP-depleted squid axons. The main observation is that Ca efflux is promoted by external Na and inhibited by internal Na. The Na0 -dependent Ca efflux appears to be a function of [Na]03, and is also affected by the membrane potential; a 25 mV depolarization may cause as much as an e-fold decrease in Ca efflux. These data are consistent with a counter-transport exchange of 3Na+-for-1Ca2+. A Ca0-dependent Ca efflux has also been observed; it is prominent in Na sea water or Le sea water, and is markedly diminished in choline sea water. This flux is consistent with the idea of a Ca-Ca exchange diffusion process. Taken together, the Na0 - and the Ca0 -dependent Ca effluxes fit a two-site model for carrier-mediated Ca transport; one site binds two Na+ or one Ca2+, while the second site can bind either one Na+ or one Li+. The data reported here suggest that both sites must be filled on the inward journey, but that only the Ca-binding site need be occupied on the outward journey of the carrier. A mechanism of this type could derive sufficient energy from the Na and voltage gradients to maintain a [Ca2+]0/[Ca2+]i concentration ratio of about 104 in the absence of ATP. The present experiments do not, however, rule out the possible participation of a metabolically driven Ca transport mechanism in vivo.
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  • 100
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    Journal of Supramolecular Structure 2 (1974), S. 737-750 
    ISSN: 0091-7419
    Keywords: Life Sciences ; Molecular Cell Biology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: We have developed methods for the isolation of Golgi apparatus from a number of mammalian tissues. The Golgi is distinct both chemically and enzymatically from the other membranes of the cell. For both liver and kidney, galactosyltransferase has been found to be a useful marker enzyme for Golgi membranes. This enzyme is involved in the modification of glycoproteins during secretion. In addition to lipoproteins and glycoproteins, the Golgi apparatus of liver is involved in the secretion of albumin, a simple protein. It does not, however, take part in the synthesis of sphingomyelin, lecithin, or triglycerides which are present in the secreted lipoproteins. These lipids appear to be synthesized predominantly by the endoplasmic reticulum. In kidney, which is rich in glycolipids, 3′-phosphoadenosine 5′-phosphosulfate, an enzyme which converts cerebroside to sulfatide, is localized predominantly in the Golgi apparatus. Thus, Golgi functions to modify glycolipids as well as mucopolysaccharides and proteins. Sulfatide constitutes a significant fraction of the total lipid of both Golgi and plasma membranes of kidney. When 35S-sulfate is injected into rats, it is incorporated first into the sulfatides of the Golgi apparatus and later appears in the sulfatides of the plasma membrane. The data are consistent with the view that sulfatides are formed in the Golgi apparatus of kidney and then transported to the plasma membrane.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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