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Zbl 0724.73159
Tsay, J.J.; Cardoso, J.E.B.; Arora, J.S.
Nonlinear structural design sensitivity analysis for path dependent problems. II: Analytical examples. (English)
[J] Comput. Methods Appl. Mech. Eng. 81, No.2, 209-228 (1990). ISSN 0045-7825

Summary: In Part 1 of this paper [see the foregoing entry (Zbl 0724.73158)] a general theory of design sensitivity analysis for nonlinear structures with history dependent effects is given. The theory is also reduced to several special cases to show its generality. In the present paper, three examples are used to analytically verify the theory. Both the adjoint structure method (ASM) and the direct differentiation method (DDM) are demonstrated. The examples are (1) reaction force sensitivity for an indeterminate beam, (2) displacement sensitivity for several cases of an axial force element and (3) stress and displacement sensitivities for a viscoelastic problem. These examples provide insights for numerical implementation of the theory for more complex design problems.

MSC 2000:: *74P99 Optimization solid mechanics
74H45 Vibrations
74S05 Finite element methods

Keywords: adjoint structure method; direct differentiation method; reaction force sensitivity; indeterminate beam; displacement sensitivity; axial force element; stress and displacement sensitivities; viscoelastic problem

Citations: Zbl 0724.73158

Cited in: Zbl 0724.73158

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