Scheme dependence and equivalence of sensitivity for nonlinear problems

In static nonlinear structural analysis, there are several schemes widely employed to calculate the responses of structures. It is known that the responses obtained are independent of the schemes chosen for the analysis problem. It is shown that if sensitivities of response variables are computed, d...

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Bibliographic Details
Published in:AIAA journal 1995-01, Vol.1 (1)
Main Authors: Leu, Liang-Jenq, Mukherjee, Subrata
Format: Article
Language:English
Online Access:Get full text
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Summary:In static nonlinear structural analysis, there are several schemes widely employed to calculate the responses of structures. It is known that the responses obtained are independent of the schemes chosen for the analysis problem. It is shown that if sensitivities of response variables are computed, different schemes do give rise, in general, to different results. However, these sensitivities are all equivalent. A systematic approach is derived to show this equivalence. This approach is derived in incremental form using the analytical differentiation approach. Numerical examples for validating the present approach include a nonlinear elastic spring model and geometric nonlinear analysis of trusses. The finite element method is used in the truss examples. It is also found that the finite difference method performs poorly in obtaining the sensitivities corresponding to the arc length and work control methods, especially for structures with limit point response. (Author)
ISSN:0001-1452