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  • 1
    Book
    Book
    Numerical methods in finite element analysis (1976)
    Englewood Cliffs, NJ :Prentice-Hall,
    Details
    Title: Numerical methods in finite element analysis
    Author: Bathe, Klaus-Jürgen
    Contributer: Wilson, Edward L.
    Publisher: Englewood Cliffs, NJ :Prentice-Hall,
    Year of publication: 1976
    Pages: 528 S.
    Type of Medium: Book
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  • 2
    Electronic Resource
    Electronic Resource
    Solution methods for eigenvalue problems in structural mechanics (1973)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 6 (1973), S. 213-226 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A survey of probably the most efficient solution methods currently in use for the problems Kφ = ω2Mφ and KΨ = λKGΨ is presented. In the eigenvalue problems the stiffness matrices K and KG and the mass matrix M can be full or banded; the mass matrix can be diagonal with zero diagonal elements. The choice is between the well-known QR method, a generalized Jacobi iteration, a new determinant search technique and an automated sub-space iteration. The system size, the bandwidth and the number of required eigenvalues and eigenvectors determine which method should be used on a particular problem. The numerical advantages of each solution technique, operation counts and storage requirements are given to establish guidelines for the selection of the appropriate algorithm. A large number of typical solution times are presented.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620060207
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The static condensation algorithm (1974)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 8 (1974), S. 198-203 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the static condensation method is discussed in general. The technique is presented as an extension of the Gauss elimination algorithm. An efficient FORTRAN subroutine is given which simultaneously reduces both the stiffness matrix and the stress-displacement transformation matrix.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620080115
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Thick shell and solid finite elements with independent rotation fields (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1393-1414 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Thick shell and solid elements presented in this work are derived from variational principles employing independent rotation fields. Both elements are built on a special hierarchical interpolation and both possess six degrees of freedom per node. Performance of the elements is evaluated on a set of problems in elastostatics. However, the formulation presented herein is also suitable for transient and non-linear problems.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310711
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Unified computational model for static and dynamic frictional contact analysis (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 34 (1992), S. 233-247 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new computational model for the analysis of friction phenomena is presented in this work. The model is a regularized form of the Coulomb friction law, which stems from the analogy of friction and plasticity phenomena. The basic difference from the classical plasticity is the non-linear form of both the normal and the tangential elastic compliance. The numerical implementation of the model is also discussed. The methodology presented herein is used for the analysis of both dynamic and quasi-static problems. The dynamic substructuring and the static condensation are used to enhance the computational efficiency.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620340115
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Finite element formulations for large deformation dynamic analysis (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 353-386 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.
    Additional Material: 18 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090207
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    A non-conforming element for stress analysis (1976)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 10 (1976), S. 1211-1219 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620100602
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Finite elements for the dynamic analysis of fluid-solid systems (1983)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 19 (1983), S. 1657-1668 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several new finite elements are presented for the idealization of two- and three-dimensional coupled fluid-solid systems subjected to static and dynamic loading. The elements are based on a displacement formulation in terms of the displacement degrees-of-freedom at the nodes of the element. The formulation includes the effects of compressible wave propagation and surface sloshing motion.The use of reduced integration techniques and the introduction of rotational constraints in the formulation of the element stiffness eliminates all unnecessary zero-energy modes. A simple method is given which allows the stability of a finite element mesh of fluid elements to be investigated prior to analysis. Hence, the previously encountered problems of ‘element locking’ and ‘hour glass’ modes have been eliminated and a condition of optimum constraint is obtained.Numerical examples are presented which illustrate the accuracy of the element. It is shown that the element behaves very well for non-rectangular geometry. The optimum constraint condition is clearly illustrated by the static solution of a rigid block floating on a mesh of fluid elements.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620191105
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    A robust quadrilateral membrane finite element with drilling degrees of freedom (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 445-457 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quadrilateral membrane finite element with drilling degrees of freedom is derived from variational principles employing an independent rotation field. Both displacement based and mixed approaches are investigated. The element exhibits excellent accuracy characteristics. When combined with a plate bending element, the element provides an efficient tool for linear analysis of shells.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620300305
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Linear and nonlinear finite element analysis on multiprocessor computer systems (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 4 (1988), S. 425-434 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several general purpose computer systems with multiple processors operating concurrently are currently being commercially produced. Most of the present generation of finite element software was not designed to take advantage of this new technology. The purpose of this paper is to present the advantages of a new architecture for finite element programs which will operate efficiently on computer systems with any number of processors. Also, the basic approach is effective for multiprocessor computers with local or shared memory.The new computer program architecture is based on an initial application of a simple algorithm which automatically subdivides the complete finite element domain into a number of subdomains equal to the number of available processors. The resulting data structure requires a minimum of communication between processors during the formation of basic element matrices, reduction of subdomain matrices and the postprocessing of element results. The assembly and solution of the global system of subdomains can be accomplished directly or iteratively, and new concurrent solution algorithms can be introduced.Several of the ideas presented here have been tested on various types of computer. The new program architecture indicates that it is possible to obtain speed-up times of over 90 per cent of the maximum theoretical values if appropriate numerical methods are employed.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630040317
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    Paper (German National Licenses)
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