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  • 1995-1999  (1,119)
  • 1996  (1,119)
  • Engineering General  (686)
  • Computational Chemistry and Molecular Modeling  (433)
  • Nuclear reactions
  • 1
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 13-20 
    ISSN: 1069-8299
    Keywords: open channel flows ; Riemann solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient numerical method is developed for the one-dimensional open channel flow equations. The scheme is a modification of one presented recently, but with an improvement in the efficiency made through the use of the arithmetic mean as an average of flow variables across the interface between adjacent states. Numerical results are shown for two problems, and an indication of the efficiency gained is given.
    Additional Material: 6 Ill.
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 21-29 
    ISSN: 1069-8299
    Keywords: finite element systems ; elliptic partial differential equations ; approximate LU factorization ; explicit matrix inversion ; preconditioning ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new class of explicit generalized approximate inverse finite element matrix algorithmic methods, based on the concept of LU-sparse factorization procedures, without inverting the decomposition factors, has recently been introduced. The large sparse unsymmetric coefficient matrix of irregular structure is factorized approximately and, in conjunction with approximate inverse matrix techniques, yields explicit preconditioned methods for the finite element (FE) and finite difference (FD) method. The numerical implementation of these algorithms is presented and Fortran subroutines for the efficient solution of the sparse unsymmetric linear systems are given.
    Additional Material: 1 Tab.
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 147-148 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 149-150 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 63-73 
    ISSN: 1069-8299
    Keywords: asymptotic solution ; natural frequencies ; membrane vibrations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper an asymptotic formula has been developed to correct the discretization error for the finite element predicted natural frequencies of membrane transverse vibration problems. The general idea behind deriving this asymptotic formula is that, when the finite element size approaches zero, a discretized finite element system approaches a continuous system and the predicted natural frequencies of the system from the finite element analysis therefore approach the exact solutions of the system. Without losing generality, several different finite element mesh patterns have been considered and the same asymptotic formula for correcting the finite element predicted natural frequency has been obtained for all the different mesh patterns because of the uniqueness of the exact solution to the natural frequency of a real structure. The usefulness, effectiveness and efficiency of the present asymptotic formula have been assessed by a simple but critical problem, for which the exact solution is available for comparison. In order to investigate the applicability of the asymptotic formula to practical engineering problems, two challenging membrane vibration problems of irregular shapes, an L-shape and a tapered shape with a circular hole in the centre, have also been analysed. The related numerical results have demonstrated that the asymptotic formula provides a very useful post-processing error corrector for the finite element predicted natural frequencies of membrane transverse vibration problems, even though the problem domains are of irregular shape. The greatest advantage in using the present asymptotic formula is that it yields a solution of higher accuracy, by simply using the formula to correct the rough solution obtained from a much coarser finite element mesh with fewer degrees of freedom, without any further finite element calculation.
    Additional Material: 7 Ill.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 107-114 
    ISSN: 1069-8299
    Keywords: beam ; vibration ; trial functions ; Ritz method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Free vibration of beams with intermediate point supports is studied by the classical Ritz method within the context of Euler beam theory. For the Ritz method, the displacement of a beam is approximated by a set of admissible trial functions which must satisfy the kinematic conditions at the ends and intermediate supports of the beam. To this end, a polynomial is superimposed on the conventional single-span beam vibration functions to form continuous-span or modified beam vibration functions. These modified beam functions are taken as the admissible trial functions for subsequent formulation. Stiffness and mass matrices are formulated using the conventional procedure and the resulting linear eigen-equation can be solved easily. A number of numerical examples are given to demonstrate the accuracy and efficiency of the present method.
    Additional Material: 3 Tab.
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  • 7
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 141-145 
    ISSN: 1069-8299
    Keywords: numerical integration ; Gauss quadrature rules ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The advance of powerful software for symbolic and numerical computations such as Mathematica sheds a new light on a paper by Golub and Welsch from 1969. Based on this paper the author describes a Mathematica procedure for determining the weights and abscissae of a Gauss quadrature rule with a user-defined weight function. After a brief description of the algorithm and its implementation examples demonstrate the usefulness of the procedure. The procedure is extremely useful if one has to compute many integrals with the same, possibly weakly singular, weight function. This might happen, for example, in the boundary element method.
    Additional Material: 1 Tab.
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  • 8
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 127-134 
    ISSN: 1069-8299
    Keywords: Laplace equation ; singularities ; boundary integral method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors present a new singular function boundary integral method for the numerical solution of problems with singularities which is based on approximation of the solution by the leading terms of the local asymptotic expansion. The essential boundary conditions are weakly enforced by means of appropriate Lagrange multipliers. The method is applied to a benchmark Laplace-equation problem, the Motz problem, giving extremely accurate estimates for the leading singular coefficients. The method converges exponentially with the number of singular functions and requires a low computational cost. Comparisons are made to the analytical solution and other numerical methods.
    Additional Material: 4 Ill.
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  • 9
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 115-125 
    ISSN: 1069-8299
    Keywords: experimental measurements ; filtering ; dynamics ; structures ; models ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a filtering algorithm which corrects the results of measurements of certain physical quantities if some information about the model of the system is known. The results of measurements are not only obtained in an explicit form for the considered variable but also in a form of dependent variables which are related to the measured quantity by certain mathematical relations. Combining the information obtained from different measurements, much better accuracy can be reached. It is proved that the proposed algorithm is able not only to enhance the measured data but also to detect the errors of the instruments.
    Additional Material: 6 Ill.
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  • 10
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 11
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 221-222 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 12
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 151-159 
    ISSN: 1069-8299
    Keywords: response reanalysis ; structural modifications ; matrix partitioning ; Sherman-Morrison formula ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper lays out an exact method, using the receptance strategy, to calculate the frequency response of a modified structure. A direct inversion of the modified impedance matrix is proposed, which reduces the computation time for successive calculations of an evolving design of the structure.
    Additional Material: 4 Ill.
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  • 13
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 175-180 
    ISSN: 1069-8299
    Keywords: permanent capillar-heavy waves ; conformal mapping ; circular shaped channels ; Zeidler's method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: E. Zeidler gave an existence and uniqueness proof for permanent heavy and capillar-heavy waves in circular shaped channels. Based on this proof and on a general computational method for constructing the solutions numerically given by the author (1991), the case of permanent heavy waves in circular shaped channels was recently computed by the author. In this work the case of permanent capillar-heavy waves in circular shaped channels is considered.
    Additional Material: 2 Ill.
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  • 14
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 161-173 
    ISSN: 1069-8299
    Keywords: inverse identification ; non-linear behaviour ; material parameters ; sensitivity analysis ; finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The identification of materials rheological behaviour in the non-linear range is based on experimental tests. When using direct identification methods, one faces the problem of the interpretation of the experimental tests, which requires the assumption of deformation homogeneity and therefore the use of approximation methods. Since this assumption is often not satisfied in the case of non-linear behaviour, material parameters are not assessed precisely. In the paper, an inverse identification method is proposed to avoid the problems raised by interpretation of the experimental tests and to determine material parameters more accurately. The algorithm developed consists of both an optimization method and a finite element method. This method is applied to the inverse identification of viscoplastic parameters of an aluminium alloy, with an investigation on the effect of the initial guess and errors in experimental data on the identified values.
    Additional Material: 5 Ill.
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  • 15
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 181-184 
    ISSN: 1069-8299
    Keywords: finite elements ; infinite elements ; mapping functions ; unbounded domains ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A few of the published three-dimensional Serendipity infinite element mapping functions have been discovered to be in error. The paper gives corrected versions of the defective mapping functions. The problems only relate to three-dimensional elements of the Serendipity type, when they extend to infinity in two or more directions. The new version of the mapping functions have been tested and appear to be robust.
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  • 16
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 185-196 
    ISSN: 1069-8299
    Keywords: homogenization ; boundary conditions ; periodicity ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of homogenization equations by the finite element (FE) method is explained briefly. The issue of extracting boundary conditions from the periodicity assumption is addressed and a direct method utilizing symmetry is presented. Using this method, the computation of the elements of the constitutive matrix of a composite material is reduced to a very conventional boundary value problem with known forces and boundary conditions which can be carried out with any FE code. Two examples are presented.
    Additional Material: 15 Ill.
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  • 17
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 18
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 269-270 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 19
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 209-220 
    ISSN: 1069-8299
    Keywords: boundary element method ; dual reciprocity ; radial basis functions ; augmented thin plate splines ; body forces ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a novel dual reciprocity formulation for elasticity problems with body forces in which the approximating functions are given in terms of augmented thin plate splines (ATPS). It is shown that the ATPS approximation is capable of correctly representing gravitational and centrifugal body forces, and provides superior accuracy for general load cases.
    Additional Material: 6 Ill.
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  • 20
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 197-208 
    ISSN: 1069-8299
    Keywords: curved surface ; triangular mesh ; automatic generation ; Bézier patches ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the discretization of any given multi-connected curved surface into triangular elements with straight sides. The method evolves from an initial rough triangular mesh generated from a set of input points which describe the geometry of the problem domain. Interior nodes are distributed according to user-established node-spacing functions of pre-specified spacing control parameters, and they are linked using the advancing front technique. Particular attention is paid to obtaining good distribution of interior nodes in the vicinity of the domain limits. Surface geometry representation is established using triangular Bézier patches with G1 continuity. This approach ensures a geometrically well-defined working platform for the subsequent discretization of the problem domain. The proposed method requires minimum input from the user and allows mesh gradation and remeshing to be carried out in a straightforward manner. Furthermore, problems associated with variations in the domain geometry as a result of local remeshing are eliminated with the aid of the geometrically pre-defined discretization platform. Results are presented for a range of both curved and planar surfaces, typical of those which might be encountered in hydrodynamics modelling involving flows with a free surface. The presented results demonstrate the flexibility and power of the technique.
    Additional Material: 11 Ill.
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  • 21
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    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 229-234 
    ISSN: 1069-8299
    Keywords: higher-order beam element ; best-fit stress prediction ; a priori error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: It is known that finite elements try to capture stresses within each discretized local region in a ‘best-fit’ sense. In the paper we examine the performance of a beam element based on a higher-order shear deformation theory and show that the best-fit paradigm accounts for the manner in which through-the-thickness displacement and stresses are modelled. An a priori prediction derived from the paradigm is confirmed by a carefully chosen numerical experiment. This provides a measure of the quality of approximation as well as another ‘falsification’ of the best-fit paradigm.
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  • 22
    Electronic Resource
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 223-228 
    ISSN: 1069-8299
    Keywords: Discretization ; heat conduction ; simulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A different approach to discretization is described with which complicated three-dimensional heat transfer problems can be solved with a finite volume approach on a general curvilinear grid. It represents an improvement on the existing methods in that it can easily be expanded to three-dimensional problems. A concise explanation of the transformation process is given, together with a discussion of the discretization procedure. The method is evaluated by solving two simple test problems and comparing the results with those of existing methods and the analytical solution. In conclusion it is found that this method yields equally or more accurate results than the existing methods, with the additional advantage of being easily expandable to three-dimensional problems.
    Additional Material: 5 Ill.
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  • 23
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 243-248 
    ISSN: 1069-8299
    Keywords: finite elements ; automatic generation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element generation methods, such as Delaunay, allow the meshing of shapes from a set of nodes. These nodes must previously exist. The authors present a simple, fast and reliable method to generate them in an unstructured way in N-dimensional space. Its main characteristic is to easily allow variation of the node density by introducing a density function, either analytical or discretized. This function can also be anisotropic. Some nodes can have a pre-fixed position. Inner lines and holes can also be specified in the domain to be meshed. Generated nodes are to be connected according to triangles in 2D and tetrahedrals in 3D.
    Additional Material: 6 Ill.
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  • 24
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 235-242 
    ISSN: 1069-8299
    Keywords: finite member element ; modified theory ; geometrical non-linearity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a modified non-linear member element is derived which can lead to satisfactory computed results even for large loading and displacement increments from pre-instability to post-instability of structures. The high accuracy of this element is proved by numerical examples.
    Additional Material: 4 Ill.
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  • 25
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 26
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 249-256 
    ISSN: 1069-8299
    Keywords: obstacle problems ; quadratic programming ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical solution of problems involving frictionless contact between an elastic body and a rigid obstacle is considered. The elastic body may undergo small or large deformation. Finite element discretization and repetitive linearization lead to a sequence of quadratic programming (QP) problems for incremental displacement. The performances of several QP algorithms, including two new versions of a modified steepest descent algorithm, are compared in this context. Numerical examples include a string, a membrane and an Euler-Bernoulli beam, in contact with flat and non-flat rigid obstacles.
    Additional Material: 2 Ill.
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  • 27
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 317-319 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 28
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 271-280 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The authors study the shape optimization of a complex cracked shell under complex criteria. The shell is one of various cases of a turboshaft, and optimization criteria are associated to the cost, the technology, and above all the working conditions for the turboshaft. The optimization criteria involved are of course the weight of the structure, but also the plastic instability and critical stress intensity factor. All computations have been made with the Ansys finite element program in which an optimization module exists.
    Additional Material: 5 Ill.
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  • 29
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 257-267 
    ISSN: 1069-8299
    Keywords: mode-matching ; Helmholtz' equation ; DtN ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element (FE) mode-matching procedures for the solution of Helmholtz' equation on an unbounded domain are reviewed and a symmetric general formulation is presented. This is a formal restatement of procedures applied previously to computations involving scattering of shallow water waves, acoustic transmission in non-uniform ducts and acoustic radiation from prismatic sheet metal ducts. An essential feature of the method is the use of a Galerkin procedure, rather than collocation, to match a finite computational model to a truncated modal expansion with the desired radiation characteristics. The method produces a symmetric set of linear equations which can be solved to give the unknown nodal values of the dependent variable and the modal coefficients of an outer expansion. Either of these sets of variables can be eliminated prior to solution to yield a reduced set of equations in the remaining parameters. The reduced equations obtained by eliminating the modal coefficients are shown to be identical to those obtained by applying a truncated Dirichlet-to-Neumann (DtN) boundary condition. If applied in this form, mode-matching can therefore be regarded as an alternative to the DtN method for generating this common set of discrete equations while permitting simultaneous solution for the modal coefficients in the outer region.
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  • 30
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 281-294 
    ISSN: 1069-8299
    Keywords: wavelets ; measures ; stability ; domains ; differential equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation.
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  • 31
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    Communications in Numerical Methods in Engineering 12 (1996), S. 371-372 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 32
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 295-302 
    ISSN: 1069-8299
    Keywords: mesh generation ; adaptivity ; iterated fractal systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the author presents a novel point of view for the refinement and derefinement algorithms of triangular nested meshes using fractal concepts and iterated function systems (IFS). The fractal behaviour can be understood in the sense that these meshes feature a remarkable amplifying invariance under changes of magnification. Here we compare the meshes obtained by the combination of these algorithms with those presented by Bova and Carey (1992). Although both of the meshes are very similar, the current algorithms automatically build and manage sequences of nested irregular discretizations of the domain. The author illustrates here how the application of IFS families is equivalent to the use of an adaptive strategy that combines the refinement procedure with the derefinement one.
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  • 33
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    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 303-316 
    ISSN: 1069-8299
    Keywords: stretching functions ; mesh refinement ; finite differences ; truncation error ; composite grids ; regularity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work the truncation-error criteria of Thompson and Mastin (1985) are combined with conditions of vanishing second and higher derivatives at both endpoints for the purpose of deriving new classes of one-dimensional stretching functions for mesh refinement in finite-difference numerics. With these elementary stretching functions, matching of the slopes between adjacent grid patches then automatically confers Cn regularity upon the composite stretching function. Formulated with reference to two conceptions of truncation order (fixed relative distribution against fixed number of nodes) the resulting mappings are shown to provide particularly advantageous node distributions at both ends simultaneously (with concomitantly higher truncation error in between). Viewed overall, the truncation-error functions compare favourably with those for sinh, tanh and erf - mappings whose utility for mesh refinement was established by Thompson and Mastin. The numerical labour of implementing the new stretching functions is only slightly greater than that required for the error function. An illustrative derivation involving Cn patching leads to two-sided stretching functions, which allow the slopes at both ends to be prescribed arbitrarily. This formulation differs from a previous approach described by Vinokur (1983).
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  • 34
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    Communications in Numerical Methods in Engineering 12 (1996), S. 331-341 
    ISSN: 1069-8299
    Keywords: glass ; finite element ; strategy's creep forming ; sheet ; manufacture ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An original optimization strategy for creep forming is carried out by finite element thermodependent viscoplastic models. For reference design glass products, an optimum forming database is developed in two steps: the first step analyses feasibility, with elastic and viscoplastic finite element models, with regard to initial manufacture choices. With thermodependent viscoplastic finite element models, the second step leads to optimum forming parameters, concerning skeleton bending radii and/or non-homogeneous heating adjustments.
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  • 35
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    Communications in Numerical Methods in Engineering 12 (1996), S. 321-330 
    ISSN: 1069-8299
    Keywords: solid-shell structure ; 3D solid element ; degenerated shell element ; DOF expanding ; multipoint constraint equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a degree of freedom expanding method for dealing with the connections of 3D isoparametric solid elements and the degenerated shell elements. By introducing two degrees of freedom to describe the elongation in the normal direction of the shell node linked with solid elements, a series of multipoint constraint equations which provide proper connections of solid and shell nodes are raised. The method gives a complete solution to the problem of connection between 3D isoparametric solid elements and degenerated shell elements even for the thermal elasto-plastic problem. It can adapt to complex junctions and simplify programming. Numerical examples are also presented to demonstrate the accuracy and feasibility in thermal elasto-plastic analysis.
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  • 36
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    Communications in Numerical Methods in Engineering 12 (1996), S. 351-357 
    ISSN: 1069-8299
    Keywords: anisotropy ; finite elements ; layers ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modification of the usual quadrangle (2D) and brick (3D) finite element for field problems is proposed. It allows the principal directions of the conductivity tensor (anisotropy directions) to be derived from the geometrical shape of the finite element and to change within it. An internal layering is assumed which is parallel to the boundary at two opposite faces (top and bottom) of the element. Without an explicit computation of angles the anisotropy directions are parallel and perpendicular to this layering. An application is the modelling of pore fluid flow in sedimentary basins.
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  • 37
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    Communications in Numerical Methods in Engineering 12 (1996), S. 343-349 
    ISSN: 1069-8299
    Keywords: mesh generation ; Delaunay mesh ; Watsens method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Automated mesh generation using a combined octree/Delaunay approach typically requires that rectangular elements be bounded by other rectangular elements which are not more that one division smaller (i.e. 1/8 the volume in 3D). This limitation is sometimes referred to as the 2 : 1 rule. This paper presents a modification which allows for any level of difference.
    Additional Material: 6 Ill.
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  • 38
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    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 39
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    Communications in Numerical Methods in Engineering 12 (1996), S. 359-369 
    ISSN: 1069-8299
    Keywords: Navier-Stokes ; artificial compressibility methodology ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the problem of laminar incompressible viscous flow through a wavy channel. An artificial compressibility method using the approximate factorization technique is applied to solve the velocity-pressure formulation of the Navier-Stokes equations written in curvilinear non-orthogonal coordinates. The physical domain used was one wavelength of the channel in which appropriate periodicity conditions were applied in order to find a solution independent of entry effects. Flow separation was observed for high Re numbers and/or large wave amplitudes of the channel. The effect of inertia to the velocity profiles was observed, and pressure and shear stress were calculated along the length of the channel. These flows have great interest in industry and medicine such as for the extracorporeal membrane oxygenator.
    Additional Material: 7 Ill.
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  • 40
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    Communications in Numerical Methods in Engineering 12 (1996), S. 445-446 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 41
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    Communications in Numerical Methods in Engineering 12 (1996), S. 383-394 
    ISSN: 1069-8299
    Keywords: symmetrically laminated plates ; anisotropy ; fundamental solutions ; boundary integral equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper the bending problem of moderately thick symmetrically laminated anisotropic plates is considered, based on the first-order transverse shear deformation plate theory. Using the method of plane wave decomposition and Hörmander's operator method, the fundamental solution of the plates is presented. The boundary integral equation of the plates is formulated by taking the fundamental solution presented as the weighted function and using the method of weighted residuals. The numerical calculation of the boundary integral equation presented is discussed in detail. Some examples are presented and compared with the exact solutions and the numerical solutions available in the literature. The numerical results show that the present method has a satisfactory rate of convergence and acceptable accuracy with a reasonable boundary mesh.
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  • 42
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    Communications in Numerical Methods in Engineering 12 (1996), S. 373-381 
    ISSN: 1069-8299
    Keywords: finite element method ; mesh refinement ; adaptivity ; singularities near edges ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with several refinement techniques of finite element meshes for treating elliptic boundary value problems in domains with re-entrant edges and corners. A priori mesh grading is explained, and it is combined with the well-known adaptive finite element method. For two representative examples the numerically determined error norms are recorded, and the different strategies are compared.
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  • 43
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    Communications in Numerical Methods in Engineering 12 (1996), S. 395-411 
    ISSN: 1069-8299
    Keywords: finite volume ; high-order discretization ; non-oscillatory schemes ; pressure interpolation ; non-staggered grid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper addresses the problem of convection discretization by extension and application of numerical schemes used in compressible flows: SONIC-A, SONIC-B, UNO2, MUSCL and MINMOD to predict steady incompressible recirculating convection dominated flows. A new scheme, SONIC-Q, is proposed together with a third-order non-oscillatory practice for pressure interpolation in non-staggered grids. Finite-volume calculations of the Navier-Stokes equations of a standard 2D driven square cavity standard test case and the laminar flow over a fence using primitive variables and non-staggered grid systems have shown that the schemes are alternatives to the conventional ones used in general algorithms for incompressible recirculating flows. In general these composite high-order schemes have proved to be good candidates to overcome the problems of false-diffusion and unboundedness encountered in non-composite high-order upwind schemes used in incompressible flows.
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  • 44
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    Communications in Numerical Methods in Engineering 12 (1996), S. 425-431 
    ISSN: 1069-8299
    Keywords: time integration ; finite element method ; least squares formulation ; multistep methods ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a formulation and analysis of three and four step least squares algorithms for first order IVPs. The three step algorithm is derived using cubic Lagrangian interpolation, and is found to be third order accurate but only conditionally stable. Fourth order Lagrangian interpolation is used to obtain a four step least squares scheme which is A0-stable but inconsistent.
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  • 45
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    Communications in Numerical Methods in Engineering 12 (1996), S. 413-424 
    ISSN: 1069-8299
    Keywords: boundary integral equation ; necessary and sufficient condition ; plane elasticity problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: With respect to a given boundary value problem, the corresponding conventional boundary integral equation is shown to yield non-equivalent solutions, which are dependent upon Poisson's ratio and geometry. In the paper a systematic method for establishing a necessary and sufficient boundary integral formulation has been proposed for two-dimensional elastostatic problems. Numerical analyses show that the conventional boundary integral equation yields incorrect results when the scale in the fundamental solution approaches a degenerate scale value. However, the results of the necessary and sufficient boundary integral equation are in good agreement with analytical solutions of the boundary value problem.
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  • 46
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    Communications in Numerical Methods in Engineering 12 (1996), S. 519-520 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 47
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    Communications in Numerical Methods in Engineering 12 (1996) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 48
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    Communications in Numerical Methods in Engineering 12 (1996), S. 433-444 
    ISSN: 1069-8299
    Keywords: two-phase flow ; solute transport ; interphase exchange ; porous media ; finite element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The development of a numerical method for modelling two-phase flows and solute transport, particularly with interphase exchange in porous media, is presented. The governing equations are derived to describe two immiscible and compressible fluids flows such as water-air and two-phase solute transport with interphase exchange. Technically, the standard finite element method and a strongly implicit procedure are employed to solve the fully coupled governing equations. Pressures of two-phase fluids and solute concentrations in two-phase fluids are taken as the primary unknown variables, and the discretized equations are solved by a direct type of solver. Application examples are shown to confirm the applicability of the numerical method.
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  • 49
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    Communications in Numerical Methods in Engineering 12 (1996), S. 447-454 
    ISSN: 1069-8299
    Keywords: inviscid drops ; coalescence ; boundary element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method is used to simulate the motion of inviscid drops colliding and coalescing at a solid surface. The equations of motion are solved by a boundary element method in which the free surface of the drop is represented by a moving grid. The numerical results include the configuration of the drop during coalescence and the kinetic and potential energies. A numerical example is used to demonstrate the way in which coalescence affects the configuration of the free surface.
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  • 50
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    Communications in Numerical Methods in Engineering 12 (1996), S. 455-459 
    ISSN: 1069-8299
    Keywords: harmonic differential quadrature method ; computational complexity ; differential quadrature ; numerical method ; centrosymmetric matrix ; computational mechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The structure of weighting coefficient matrices of harmonic differential quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric, depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in the paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced by up to 75 per cent by using the properties of the above-mentioned matrices.
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  • 51
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    Communications in Numerical Methods in Engineering 12 (1996), S. 471-482 
    ISSN: 1069-8299
    Keywords: numerical methods ; constitutive equations ; composite ; mixing formulation ; anisotropic elastoplastic model ; mapping stress tensor space ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general constitutive model adequate for analysis of the thermomechanical response of composite materials is presented. The model is based on the mixture of the basic substances of the composite and allows the evaluation of the interdependence between the constitutive behaviour of different compounding materials. The behaviour of the each compound is modelled by a general anisotropic thermo-elasto-plastic model, termed the ‘base model’. The different base models for each compound are combined using mixing theory to simulate the behaviour of the multiphase material.
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  • 52
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    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
    ISSN: 1069-8299
    Keywords: finite element method ; solid modelling ; optimal interpolation ; a posteriori error estimation ; adaptive interpolation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.
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  • 53
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    Communications in Numerical Methods in Engineering 12 (1996), S. 461-470 
    ISSN: 1069-8299
    Keywords: linear polyhedra ; symbolic integration ; polynomial functions ; monomials ; tetrahedron ; hexahedron ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper concerns analytical integration of polynomial functions over linear polyhedra in three-dimensional space. To the authors' knowledge this is a first presentation of the analytical integration of monomials over a tetrahedral solid in 3D space. A linear polyhedron can be obtained by decomposing it into a set of solid tetrahedrons, but the division of a linear polyhedral solid in 3D space into tetrahedra sometimes presents difficulties of visualization and could easily lead to errors in nodal numbering, etc We have taken this into account and also the linearity property of integration to derive a symbolic integration formula for linear hexahedra in 3D space. We have also used yet another fact that a hexahedron could be built up in two, and only two, distinct ways from five tetrahedral shaped elements These symbolic integration formulas are then followed by an illustrative numerical example for a rectangular prism element, which clearly verifies the formulas derived for the tetrahedron and hexahedron elements.
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  • 54
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    Communications in Numerical Methods in Engineering 12 (1996), S. 497-505 
    ISSN: 1069-8299
    Keywords: weight function approach ; edge crack problem ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A fundamental field for the edge crack problem is suggested, and the field is composed of the singular displacement field and the complementary regular field. The boundary displacement of the fundamental field plays the role of the weight function in the edge crack problem. After multiplying the boundary traction in the physical problem with the weight function and performing integration along the boundary, the stress intensity factor at the crack tip is obtainable. Numerical examples are given to demonstrate the use of the suggested weight function approach.
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  • 55
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    Communications in Numerical Methods in Engineering 12 (1996), S. 543-555 
    ISSN: 1069-8299
    Keywords: control volume method ; finite element interpolation ; fluid flow ; upwind schemes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Together with the finite element method (FEM), the control volume method (CVM) is of particular interest for the numerical solution of partial differential equations. The accuracy of computation of the CVM almost matches that of FEM in contour-adapted co-ordinates or block-structured meshes of a single element type. The CVM is superior to the FEM in terms of physical interpretation and ease of handling. The paper presents an interpretation of the FEM that allows it to be treated like a CVM. This formal CVM, which is based on FEM techniques, combines the advantages of both methods. The method is applied to the discretization of the Navier-Stokes equation.
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  • 56
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    Communications in Numerical Methods in Engineering 12 (1996), S. 557-568 
    ISSN: 1069-8299
    Keywords: hyperbolic equations ; finite-difference methods ; Padé approximants ; sequential and parallel implementation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for two-time level difference schemes are presented for the numerical solution of first-order hyperbolic partial differential equations. The space derivative is approximated by (i) a low-order, and (ii) a higher-order backward difference replacement, resulting in a system of first-order ordinary differential equations, the solutions of which satisfy recurrence relations. The methods are obtained from the recurrence relations and are tested on three linear problems and one non-linear problem from the literature.
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  • 57
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    Communications in Numerical Methods in Engineering 12 (1996), S. 507-517 
    ISSN: 1069-8299
    Keywords: non-linear constitutive model ; anisotropy ; finite strains ; axisymmetrical finite elements ; vascular biomechanics ; soft tissue biomechanics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To explore the mechanical non-linear behaviour of anisotropic arterial walls on a computational basis, the formulation of a continuum based elastic potential is a major task and challenge to the analyst. The present communication is concerned with the constitutive modelling and numerical analysis of vascular segments covering finite strains. Special attention is paid to a two term potential that constitutes an essential foundation for accurate simulation within the entire strain domain. Axisymmetrical membrane elements are assembled to match the geometry of blood vessels. Numerical results confirm the theoretical approach by referring to experimental data of different rat arteries.
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  • 58
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    Communications in Numerical Methods in Engineering 12 (1996), S. 569-579 
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    Keywords: frictional contact ; large deformation ; one-pass approach ; master segment ; slave node ; contact constraint ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the context of large deformation analysis for metal forming processes a new one-pass approach for the frictional contact is proposed. This approach eliminates the short comings of traditional one-pass and two-pass approaches both from the constraint requirement and solution convergence points of view. Implemented in an updated Lagrangian framework with the Perturbed Lagrangian formulation of Ju and Taylor for non-linear frictional contact, a patch test and typical examples have been worked out to prove the validity of the proposed approach. It is observed that a finer surface discretization of the slave and master surfaces is no longer needed to enforce contact constraint.
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  • 59
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    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    ISSN: 1069-8299
    Keywords: acoustics ; finite element method ; error estimation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A posteriori error estimation has become very popular, mainly in linear elasticity. A robust implementation of the superconvergent patch recovery technique of O. C. Zienkiewicz and J. Z. Zhu is presented for acoustic finite element analyses: the original concepts are extended to complex variables, and both local and global behaviours of the recovery procedure and the error estimation are studied. The numerical tests confirm the improvement of the rates of convergence for the recovered solution and also show the reliability of the error estimator except at frequencies corresponding either to the analytical or to the finite element eigenfrequencies.
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  • 60
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    Communications in Numerical Methods in Engineering 12 (1996), S. 595-595 
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    Keywords: Engineering ; Engineering General
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  • 61
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    Communications in Numerical Methods in Engineering 12 (1996) 
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    Keywords: Engineering ; Engineering General
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  • 62
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    Communications in Numerical Methods in Engineering 12 (1996), S. 599-608 
    ISSN: 1069-8299
    Keywords: finite elements ; moving grids ; moving bodies ; mesh velocity ; ALE ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether.
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  • 63
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    Communications in Numerical Methods in Engineering 12 (1996), S. 767-773 
    ISSN: 1069-8299
    Keywords: curved beam element ; membrane locking ; shear locking ; strain based element ; transformation matrix ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Two curved beam elements with two nodes and three nodes are designed based on strain fields. At the element level, curvature and membrane strain fields are approximated independently and shear strain fields are incorporated into the formulation by the equilibrium equations. The displacement fields are obtained by integrating the assumed strain fields. Two examples are given to verify the formulations and demonstrate the numerical performance of the two curved beam elements. Analysis results obtained reveal that the elements describe the curved beam behaviour correctly and show exceptional accuracy throughout a wide slenderness range.
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    Communications in Numerical Methods in Engineering 12 (1996), S. 775-785 
    ISSN: 1069-8299
    Keywords: membrane ; wrinkle ; non-linear ; elasticity ; finite-element method ; sail ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is a presentation of a quadrilateral finite element for wrinkled curved elastic membranes. A modified form of the deformation gradient enables us to avoid the spurious compressive stresses generated by a classical model. It results in non-linear relations for the eigencomponents of the Cauchy stress tensor, which are solved by means of a secant method. The application of the element to sail design is presented in this paper.
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  • 65
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    Communications in Numerical Methods in Engineering 12 (1996), S. 795-804 
    ISSN: 1069-8299
    Keywords: RLW equation ; finite element methods ; Petrov-Galerkin ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation functions. In addition, for very small amplitude waves (≤ 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The development of an undular bore is modelled.
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  • 66
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    Communications in Numerical Methods in Engineering 12 (1996), S. 787-793 
    ISSN: 1069-8299
    Keywords: regularization ; boundary integral equations ; hypersingular integrals ; Hadamard finite part ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Strongly singular integrals which are unbounded in the sense of Lebesgue appear naturally in boundary integral equations. Extending the analytic continuation method we derive finite part values for a class of singular integrals which arise frequently in practice. In connection with boundary integral operators we derive restrictions on the minimum smoothness of the density functions for the validity of the finite part results. Examples of applications of the results to boundary integral equations in potential theory are presented.
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  • 67
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    Communications in Numerical Methods in Engineering 12 (1996) 
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    Keywords: Engineering ; Engineering General
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    Communications in Numerical Methods in Engineering 12 (1996), S. 805-805 
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    Keywords: Engineering ; Engineering General
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    Communications in Numerical Methods in Engineering 12 (1996), S. 827-834 
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    Keywords: stress-strain relationship ; monotonic loading ; failure stress ; failure strain ; initial modulus ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A function containing four parameters allowing close approximation of experimental stress-strain relationships is presented. The parameters are easily determined from corresponding conditions at the ends and inside of the total interval of the strain variation from zero stain up to failure stain. The family of curves obtained covers an area on the stress-strain plane where any acceptable stress-strain curve can pass. The softening behaviour of soils can also be taken into consideration.
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  • 70
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    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    ISSN: 1069-8299
    Keywords: incompressible materials ; finite element method ; p-version ; elasticity ; stress extraction ; complementary energy ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Direct methods for computing the pointwise stresses for nearly incompressible elastic materials fail to provide meaningful results when applied to the displacement formulation of the finite element method (FEM). A new extraction method for accurate computation of pointwise stresses for nearly incompressible elastic materials is presented. It is based on the complementary energy principle applied over a local domain in the postprocessing phase in conjunction with the p-version finite element solution. It is shown that accurate pointwise stresses are obtained, that the relative error in the pointwise stresses converges at a rate which is as fast as the relative error measured in the energy norm or faster, and importantly, the extracted stresses are virtually independent of Poisson's ratio. Numerical results for two problems, one having a smooth solution and the other containing a singular point, are provided.
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  • 71
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    Communications in Numerical Methods in Engineering 12 (1996), S. 835-847 
    ISSN: 1069-8299
    Keywords: superposition method ; perturbation of eigenvectors ; structural modification ; basis ofN-dimension Euclidean space ; orthogonalization of Schmit procedure ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The modal superposition method is often used for computing the perturbation of eigenvectors in structural modification and model correction. However, it will bring about significant errors in the solution when the high-frequency modes are truncated. This paper presents a new method, which uses known modes construct a new basis of the N-dimensional Euclidean space (say, the mixed-basis), to calculate the first and second order perturbations of the known eigenvectors. In the present method only the known modes are used. The accuracy of this method not only has no relation to number of the truncated modes but is better than the truncated modal superposition method, in which only the known modes are employed. A numerical example of a truss structure with 36 degrees of freedom is given to illustrate the effectiveness of the method.
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  • 72
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    Communications in Numerical Methods in Engineering 12 (1996), S. 849-862 
    ISSN: 1069-8299
    Keywords: superconvergence ; isoparametric bilinear finite elements ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper the superconvergence property of isoparametric bilinear finite elements is considered. A new superconvergence recovery method for isoparametric bilinear finite elements is discovered on the four vertices and the four midpoints of the edges of the elements for piecewise strongly regular quadrilateral subdivisions.
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  • 73
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    Communications in Numerical Methods in Engineering 12 (1996) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 74
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    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
    ISSN: 1069-8299
    Keywords: thin-walled beam ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method for computing the deformation of thin-walled beams with closed cross-section under warping torsional loading is presented. In comparison to the classical theory (Umanski), the hypothesis of no deformation of the contour of the cross-section of the beam is maintained and the assumption of no distortion of the cross-section plane is modified. The new approach gives better results than the classical theory when both are compared to a standard finite element technique (using shell elements). The central idea of the new approach lies in the usage of a new finite element called a macro-element, which is especially well suited for thin-walled beam computations.
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  • 75
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    Communications in Numerical Methods in Engineering 12 (1996), S. 135-140 
    ISSN: 1069-8299
    Keywords: finite elements ; QUAD4 elements ; RBF corrections ; shear force predictions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The residual bending flexibility correction is an extra-variational trick used to enhance the convergence rate of shear flexible beam and plate elements. In the paper we show how this can affect the shear deflection and shear force estimates in the QUAD4 element.
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  • 76
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    Communications in Numerical Methods in Engineering 12 (1996), S. 597-597 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 77
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    Communications in Numerical Methods in Engineering 12 (1996), S. 521-529 
    ISSN: 1069-8299
    Keywords: bellows ; shell of revolution ; integral equation method ; compressed angle ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a U-shaped bellows is treated as a flexible shell of revolution which consists of circular ring shells and truncated shallow conical shells; then the non-linear problem of U-shaped bellows under the action of axial compression force and internal pressure is solved by means of the non-linear theory of shells and the integral equation method. Numerical solutions obtained are compared with previous theoretical and experimental results. The present theory is more appropriate to the analysis of bellows in the light of real profile shape, and shows that the influence of compressed angle on the characteristic relation and peak stresses is noticeable.
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  • 78
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    Communications in Numerical Methods in Engineering 12 (1996), S. 531-542 
    ISSN: 1069-8299
    Keywords: vibration ; inverse eigenvalue problem ; modal analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method for determining mass and stiffness modifications to achieve desired natural frequencies is presented. The given data are modal testing results, which consist of a truncated set of natural frequencies and mode shapes. The difficulty arising from the incompleteness of data is overcome by solving an optimization problem rather than seeking an exact solution. The obtained modifications are optimal in a Rayleigh-Ritz sense. The case where the mass and stiffness matrices are interrelated is also considered. Numerical examples demonstrating the various results and the sensitivity of the problem to perturbations are presented.
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  • 79
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    Communications in Numerical Methods in Engineering 12 (1996), S. 609-616 
    ISSN: 1069-8299
    Keywords: hybrid-Trefftz element ; plate ; transient analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a hybrid Trefftz (HT) element approach for the numerical solution of transient plate bending problems. In the proposed method, the dynamic plate equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. Two examples are considered to assess the effectiveness of the numerical method.
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  • 80
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    Communications in Numerical Methods in Engineering 12 (1996), S. 617-630 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three different solution methods for the finite-volume discretized incompressible Navier-Stokes equations have been tested: segregated approaches, built around coupling methods such as SIMPLE, SIMPLER and PISO plus a line Gauss-Seidel linear solver; coupled methods, incorporating a penalty formulation to eliminate zero diagonal elements in the coefficient matrices, plus preconditioned GMRES as a linear solver;- and a FAS-full multigrid algorithm accelerating a classical segregated method based upon SIMPLE and the line Gauss-Seidel solver. Results demonstrate that the coupled method compares favourably to the segregated technique at small grid sizes but becomes too expensive for large problems. The FAS-full multigrid algorithm outperforms the other two methods when large numbers of nodes are employed in the simulation.
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  • 81
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    Communications in Numerical Methods in Engineering 12 (1996), S. 631-641 
    ISSN: 1069-8299
    Keywords: numerical analysis ; fast direct method ; elliptic problems ; finite difference methods ; eigenvalue problems ; harmonic ; biharmonic ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A high accuracy finite difference scheme has been developed for solving some elliptic problems which appear in engineering and applied sciences. These include Laplace, Poisson, Helmholtz and related equations. The second- and fourth-order problems dealing with vibration of membranes and plates have also been examined. Numerically, the problem reduces to a block tridiagonal system which can be solved by suitably modifying the fast direct method developed by Hockney. Comparison has been made with results obtained from some alternative numerical methods or analytical methods whenever available
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  • 82
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    Communications in Numerical Methods in Engineering 12 (1996), S. 643-655 
    ISSN: 1069-8299
    Keywords: viscoelastic flows ; sphere ; annular flow ; adaptive meshing ; finite elements ; error analysis ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This work describes the implementation of an adaptive procedure for viscoelastic flows. Finite element simulations are conducted using a Taylor-Galerkin/pressure correction scheme. The constitutive equations considered are those for an Oldroyd-B and a Phan-Thien/Tanner model. The adaptive meshing technique is h-refined by grid remeshing, based on a Delaunay procedure. Results are presented for two benchmark problems, namely flow past a sphere in a cylindrical tube and flow in an annular converging tube. It is concluded from the results that the use of an adaptive procedure with mesh regeneration enables an optimized mesh to be devised and a predicted accuracy to be attained.
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  • 83
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    Communications in Numerical Methods in Engineering 12 (1996), S. 657-671 
    ISSN: 1069-8299
    Keywords: continuous casting ; free boundary problem ; co-ordinate transformation ; solidification front ; non-orthogonal control volume ; temperature profile ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient computational simulation scheme based on non-orthogonal control volume discretization and co-ordinate transformation techniques has been developed for solving the thermal transport phenomena, which involves tracking of the interface between solid and liquid phases (solidification front) and evaluation of the temperature profile during continuous casting operation. Conservation equations are reformulated in differential-integral form in terms of the transformed co-ordinates. All the terms arising from the non-orthogonality of the control volume have been retained in the numerical solution methodology, and a front tracking procedure has been formulated based on an iterative solution scheme. The formulation has been applied to solve the thermal transport phenomena in solidification processing of an A1-Mg alloy cylindrical ingot during continuous casting, which also includes axial conduction of heat. Theoretical evaluation of the solidification front and temperature distribution in the ingot are in good agreement with the experimentally measured data.
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  • 84
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    Communications in Numerical Methods in Engineering 12 (1996) 
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    Keywords: Engineering ; Engineering General
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  • 85
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    Communications in Numerical Methods in Engineering 12 (1996), S. 673-682 
    ISSN: 1069-8299
    Keywords: temperature field ; heat source ; IBEM ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The fundamental solution of the temperature field in an infinite three-dimensional body under the periodic unit thermal source is given in the present paper. According to the indirect boundary element method (IBEM) with fictitious heat sources, the problem of 3-D periodic heat conduction in a finite body is solved. By use of a quadratic inharmonic element, the problem of the corner region and the indetermination of the normal direction at boundary points can be solved in the numerical process. The validity of the present method is checked with two examples of which analytical solutions exist. It offers a useful method for the actual simulated calculation of the 3-D temperature field in engineering.
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  • 86
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    Communications in Numerical Methods in Engineering 12 (1996), S. 703-703 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 87
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    Communications in Numerical Methods in Engineering 12 (1996), S. 705-705 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 88
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    Communications in Numerical Methods in Engineering 12 (1996), S. 707-717 
    ISSN: 1069-8299
    Keywords: hybrid element ; shear locking ; penalty-equilibrating approach ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents a penalty-equilibrating approach which is used to enforce the equilibrium constraints to individual hybrid elements so as to optimize the element performance. The approach has been applied successfully to improve the 4-noded hybrid stress membrane element (P-S) by Pian and Sumihara. It turns out that some defects of the P-S element, e.g. the shear locking phenomenon and the inability to pass the MacNeal's bending test, can be overcome and the element performance is significantly improved, without having to add any extra variables to the P-S element or to modify its stress fields.
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  • 89
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    Communications in Numerical Methods in Engineering 12 (1996), S. 683-702 
    ISSN: 1069-8299
    Keywords: unstructured grid generation ; finite elements ; advancing front ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We describe extensions and improvements to the advancing front grid generation technique that have proven useful over the years. The following areas are treated in detail: situations with thin or crossing surfaces, meshing of surfaces defined by triangulations, and ease of user input to define the desired element size in space. The first extension is important if one considers the generation of volumetric grids around shells, membranes, fabrics, or CAD-data that exhibit cusps. Traditional advancing front generators are likely to fail in these situations. We propose the introduction of a crossing environment variable attached to faces and points in order to filter out undesired or incorrect information during the grid generation process. The second extension is required for situations where the surfaces to be gridded are not defined analytically, but via a triangulation. Typical cases where such triangulations are used to define the domain are geophysical problems, climate modelling and medical problems. The third topic deals with the reduction of manual labour to specify element size in space. Sources, element size attached directly to CAD-data, and adaptive background grids are discussed. Adaptive background grids, in combination with surface deviation tolerances, are used to obtain surface triangulations that represent the geometry faithfully, and at the same time enable a smooth transition to volumetric meshes.
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  • 90
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    Communications in Numerical Methods in Engineering 12 (1996), S. 731-743 
    ISSN: 1069-8299
    Keywords: explicit integration ; finite elements ; stiffness matrix ; symbolic manipulation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with the symbolic integration of a 4-noded isoparametric finite element for plane elasticity. An efficient approach to generate explicit formulas for computing the elementary stiffness matrix is discussed. The procedure is based on the use of the Derive symbolic manipulation code as well as in a posteriori manipulation of the expressions obtained. The accuracy of the results is tested in extremely distorted and geometrically ill-conditioned elements. Three practical engineering models are presented and the accuracy of the results is discussed. A computer time comparison between both numerical and symbolic integration approaches is also included, showing that relevant CPU savings are obtained when applying symbolic integration.
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  • 91
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    Communications in Numerical Methods in Engineering 12 (1996), S. 719-729 
    ISSN: 1069-8299
    Keywords: air humidification process ; experiments ; predictions with finite-difference technique ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with a numerical and an experimental analysis of the humidification process of air in a nearly horizontal tube. The numerical analysis is based on a finite-difference solution of the three-dimensional momentum, heat and mass transfer differential equations within the tube for the evaporation process of a water stream of circular meniscus cross-section counterflowing to an air stream. In order to provide reliable, high-accuracy data to assist in the development of the theoretical model, tests have been conducted using specially constructed apparatus to measure temperature and velocity profiles within the tube. The proposed computer algorithm was validated by evaluating its ability to predict the measurements of temperatures and velocities along the stream's flow. The theoretical predictions agree well with the experimental data. The model may be used to give performance characteristics for a wide range of humidification processes with different working fluids and state conditions.
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  • 92
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    Communications in Numerical Methods in Engineering 12 (1996), S. 745-753 
    ISSN: 1069-8299
    Keywords: boundary element method ; foundations ; soil-structure interaction ; contact problem ; optimal solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The problem of providing settlement uniformity of a rigid foundation on a non-uniformly compressible base has been reduced to the contact problem from elasticity theory, with controlling parameters which allow one to select either co-ordinates of the point of application of the vertical load resultant or contours in plan at which the foundation slope will be equal to zero. The solution of the problem is illustrated by numerical examples.
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  • 93
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    Communications in Numerical Methods in Engineering 12 (1996), S. 755-766 
    ISSN: 1069-8299
    Keywords: finite elements ; isoparametric ; Jacobian ; transformation ; valid ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Isoparametric elements are only valid if the Jacobian determinant of the transformation between a given element and a master element does not change sign within or on the element boundary. Some algorithms are known which analyse Jacobians for various element types. Some necessary conditions are presented for determining the validity of an element.
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  • 94
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    Communications in Numerical Methods in Engineering 12 (1996), S. 885-896 
    ISSN: 1069-8299
    Keywords: interfaces ; sliding ; contact ; impact ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an automatic sliding interface algorithm for intense impulsive loading computations due to high velocity impact and explosive detonation. This algorithm allows the user to perform computations involving complex sliding interfaces without having to predetermine the sliding interfaces; everything is automated. The interface determination algorithm, the searching algorithm and the contact algorithm are included.
    Additional Material: 7 Ill.
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  • 95
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    Communications in Numerical Methods in Engineering 12 (1996), S. 863-871 
    ISSN: 1069-8299
    Keywords: objectivity ; kinematics ; computational mechanics ; large deformations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an example problem is presented that illustrates the importance of strong objectivity in kinematic algorithms for large-deformation finite element applications. The example problem involves cyclic simple shearing of a hypoelastic material, wherein the increments of stretch and of rotation are of comparable magnitude. It is demonstrated that two kinematic algorithms that are in common use, and which are only weakly objective, give rise to an accumulative error in the normal stress components. The error is surprisingly large, even for very small strain increments. This behaviour arises due to a coupling between the stretch and rotation increments that is exhibited by weakly objective algorithms, and is perhaps especially serious in the context of models for jointed rock and other frictional materials, in which the shear response may depend strongly on the normal components of stress.
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  • 96
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    Communications in Numerical Methods in Engineering 12 (1996), S. 905-905 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 97
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    Communications in Numerical Methods in Engineering 12 (1996), S. 897-903 
    ISSN: 1069-8299
    Keywords: finite element analysis ; reinforced concrete element ; embedded reinforcement ; stress analysis ; brick element ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper a mathematical formulation for embedding reinforcements in 3D brick concrete elements is presented. The computational aspects and the implementation process of the model have been discussed. The proposed algorithm may be implemented in 3D finite element programs for stress analysis of reinforced concrete structures.
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  • 98
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    International Journal of Quantum Chemistry 57 (1996), S. 7-15 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The solution of the Schrödinger equation for the d-dimensional hydrogen atom in a d-dependent potential defined by Gauss' law has been studied by the shifted 1/d method and the δ expansion. These methods provide analytical formulas for the eigenvalues and eigenfunctions which have been tested against “exact” numerical values obtained recently. The comparison shows that the results obtained with the analytical expressions are in excellent accord with the numerical ones and, on the other hand, provide a theoretical justification for a proposed empirical expression for the energies of the two-dimensional hydrogen atom with a logarithmic potential energy function. © 1996 John Wiley & Sons, Inc.
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  • 99
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    International Journal of Quantum Chemistry 57 (1996), S. 17-33 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An analysis of the structure of the optimized effective Kohn-Sham exchange potential vx and its gradient approximations is presented. The potential is decomposed into the Slater potential vs and the response of vs to density variations, vresp. The latter exhibits peaks that reflect the atomic shell structure. Kohn - Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of vx with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact vx. © 1996 John Wiley & Sons, Inc.
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  • 100
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    International Journal of Quantum Chemistry 57 (1996), S. 43-51 
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Analytical exact expressions are obtained for matrix elements of the modified Pöschl-Teller oscillator over different operators including powers of the hyperbolic functions sinh(α x), cosh(α x), and tanh(α x) and the differential operators d/dx and d2/dx2. These expressions are derived using explicitly the Pöschl-Teller eigenfunctions. In addition, several recursion relations connecting different Pöschl-Teller matrix elements are obtained using the factorization and hypervirial techniques. It is shown that these relations can be used to make easier the computation of the matrix elements. © 1996 John Wiley & Sons, Inc.
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