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A continuum‐based shell theory for non‐linear applications
Author(s) -
Parisch H.
Publication year - 1995
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620381105
Subject(s) - stress resultants , quadrilateral , finite element method , shell (structure) , nonlinear system , degrees of freedom (physics and chemistry) , shell theory , development (topology) , computer science , mathematics , structural engineering , engineering , mechanical engineering , mathematical analysis , physics , quantum mechanics
The paper introduces a non‐linear shell theory, which provides a complete three‐dimensional state of stress. Since the theory is derived from simple three‐dimensional continuum mechanics, it is very easy to understand. As an example, the theory is applied to quadrilateral shell elements, which provide only displacement degrees of freedom located at nodes on the outer surfaces and one degree of freedom at the middle surface. It is proposed to eliminate this degree of freedom on element level, so that the elements have the same layout as the equivalent brick elements, but have a better behaviour in bending, have stress resultants and are cheaper with respect to computational effort. The advantages with respect to implementation in a finite element program, as well as in special applications, are obvious. However, well‐known conditioning problems in thin shell applications must be expected. Therefore emphasis is put on this issue in the example problems. It is shown that the elements can give acceptable answers in engineering applications and offer a potential for material non‐linear applications, which will be considered in a forthcoming paper.