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  • 1
    Electronic Resource
    Electronic Resource
    Modified calculation of the dissipation term in thermoplastic finite element equations (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 69-72 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; thermoplasticity ; internal dissipation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110110
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  • 2
    Electronic Resource
    Electronic Resource
    The variationally correct rate of convergence for a two-noded beam element, or why residual bending flexibility correction is an extravariational trick (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 403-407 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; residual bending flexibility ; convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640110504
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  • 3
    Electronic Resource
    Electronic Resource
    Comparison of several mesh refinement strategies near edges (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 373-381 
    Details
    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.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Three and four step least squares finite element schemes in the time domain (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 425-431 
    Details
    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.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Adaptive procedure for approximating functions by continuous piecewise polynomials (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 483-495 
    Details
    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.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Superconvergent patch recovery technique for the finite element method in acoustics (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 581-594 
    Details
    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.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Accurate stress extraction for nearly incompressible materials by the displacement formulation of the p-version FEM (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 807-826 
    Details
    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.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Study of warping torsion of thin-walled beams with closed cross-section using macro-elements (1996)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 12 (1996), S. 873-884 
    Details
    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.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    IMPROVING MODULARITY IN OBJECT-ORIENTED FINITE ELEMENT PROGRAMMING (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 193-198 
    Details
    ISSN: 1069-8299
    Keywords: finite element method ; software engineering ; object-oriented programming ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Making a finite element code easier to maintain is achieved by further modularizing it. Due to its two levels of modularity (of procedures and data), object-oriented programming is the method of choice. Its potential is investigated in two bottlenecks of finite element programming where so far it has not proved significantly more successful than classical Fortran programming. The first of these is the lack of adequate data structures between the analysis specifications and the basic objects of the finite element method, like the element and the node. This is solved by defining two classes of objects, namely problem and domain, with clearly differentiated specifications. The second gap deals with solving linear equation systems. Introducing an intermediate class UnassembledMatrix allows alternative storage/solving schemes to be implemented in a very flexible manner. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    AN EXACT STRUCTURAL STATIC REANALYSIS METHOD (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 103-112 
    Details
    ISSN: 1069-8299
    Keywords: static reanalysis ; finite element method ; structural analysis ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an exact structural static reanalysis method for locally modified structures. Through the introduction of structural rigid body motion eigenvectors, the generalized structural compliance matrix can be obtained and the original stiffness equation is transformed into a linear system of much lower order. The general solution of displacements can be expressed prior to any assignment of boundary conditions. For a structure with given boundary and loading conditions, the displacements can be obtained by solving this linear system. For locally modified structures, the structural compliance matrix can be adjusted quickly. This static reanalysis method can be used for structures with modifications on structural elements, boundary and loading conditions, either independently or in combination. Two test examples are provided in the paper to prove the efficiency of the method. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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