Large natural strains and some special difficulties due to non-linearity and incompressibility in finite elements

The finite element method is now a well established tool for the routine treatment of large linear problems, but the treatment of non-linear problems by the method is yet at the beginning. Section 1 of the present work extends the idea of natural strains and stresses to large strains in simplex fini...

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Published inComputer methods in applied mechanics and engineering Vol. 4; no. 2; pp. 219 - 278
Main Authors Argyris, J.H., Dunne, P.C., Angelopoulos, T., Bichat, B.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.1974
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ISSN0045-7825
1879-2138
DOI10.1016/0045-7825(74)90035-8

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Summary:The finite element method is now a well established tool for the routine treatment of large linear problems, but the treatment of non-linear problems by the method is yet at the beginning. Section 1 of the present work extends the idea of natural strains and stresses to large strains in simplex finite elements. Section 2 applies some algorithms developed for structural dynamics to the problem of non-linear wave propagation including a case of shock development. Section 3 discusses with numerical examples special difficulties when displacement finite elements are used to solve problems with incompressible or nearly incompressible material.
Bibliography:ObjectType-Article-2
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ISSN:0045-7825
1879-2138
DOI:10.1016/0045-7825(74)90035-8