Non-iterative solution of finite-element equations in incompressible solids

    Authors

    D. W. Nicholson

    Comments

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    Abbreviated Journal Title

    Acta Mech.

    Keywords

    Mechanics

    Abstract

    Finite-element equations for incompressible and near-incompressible media give rise to a matrix with a diagonal block of zeroes or very small numbers. The matrices are not amenable to conventional techniques involving pivoting on diagonal entries. Uzawa methods have been applied to the associated linear systems. They are iterative and converge when the matrix is nonsingular. In the current study an alternate form of the matrix is used which is amenable to a solution without iteration. It likewise is applicable whenever the matrix is nonsingular. The solution process consists of a block LU factorization, followed by Cholesky decomposition of a positive definite diagonal block together with several forward and backward substitution operations. Two illustrative examples are developed.

    Journal Title

    Acta Mechanica

    Volume

    167

    Issue/Number

    3-4

    Publication Date

    1-1-2004

    Document Type

    Article

    Language

    English

    First Page

    189

    Last Page

    195

    WOS Identifier

    WOS:000220264400005

    ISSN

    0001-5970

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