Premium
A fully non‐linear axisymmetrical quasi‐kirchhoff‐type shell element for rubber‐like materials
Author(s) -
Eberlein R.,
Wriggers P.,
Taylor R. L.
Publication year - 1993
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.1620362307
Subject(s) - linearization , finite element method , ogden , mathematical analysis , shell (structure) , mathematics , quadratic equation , computation , conical surface , geometry , nonlinear system , structural engineering , physics , engineering , civil engineering , algorithm , quantum mechanics , thermodynamics
An axisymmetrical shell element for large deformations is developed by using Ogden's non‐linear elastic material law. This constitutive equation, however, demands the neglect of transverse shear deformations in order to yield a consistent theory. Therefore, the theory can be applied to thin shells only. Eventually a ‘quasi‐Kirchhoff‐type theory’ emerges. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non‐linear bending behaviour. Furthermore, special attention is paid to the linearization procedure in order to obtain quadratic convergence behaviour within Newton's method. Finally, the finite element formulation for a conical two‐node element is given. Several examples show the applicability and performance of the proposed formulation.