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On evaluation of shape sensitivities of non‐linear critical loads
Author(s) -
Parente E.,
Vaz L. E.
Publication year - 2002
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.587
Subject(s) - computation , sensitivity (control systems) , limit load , limit (mathematics) , finite element method , shape optimization , bifurcation , mathematical optimization , mathematics , computer science , element (criminal law) , algorithm , structural engineering , nonlinear system , engineering , mathematical analysis , physics , quantum mechanics , electronic engineering , political science , law
The present paper focuses on the evaluation of the shape sensitivities of the limit and bifurcation loads of geometrically non‐linear structures. The analytical approach is applied for isoparametric elements, leading to exact results for a given mesh. Since this approach is difficult to apply to other element types, the semi‐analytical method has been widely used for shape sensitivity computation. This method combines ease of implementation with computational efficiency, but presents severe accuracy problems. Thus, a general procedure to improve the semi‐analytical sensitivities of the non‐linear critical loads is presented. The numerical examples show that this procedure leads to sensitivities with sufficient accuracy for shape optimization applications. Copyright © 2002 John Wiley & Sons, Ltd.