Title

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

Authors

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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