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Zbl 0724.73158
Tsay, J.J.; Arora, J.S.
Nonlinear structural design sensitivity analysis for path dependent problems. I: General theory. (English)
[J] Comput. Methods Appl. Mech. Eng. 81, No.2, 183-208 (1990). ISSN 0045-7825

Summary: Two procedures (direct differentiation and adjoint structure) for design sensitivity analysis of nonlinear structural systems with path dependent effects are described in this paper. Continuum formulation is used and both geometric and material nonlinearities are included in the derivations. Incremental nonlinear analysis based on the total Lagrangian concept is adopted. The reference volume concept is used to unify the shape and nonshape design problems. To show the generality of the theory, the derived expressions are reduced to some special cases that have been treated previously in the literature. In Part 2 of the paper a few analytical example problems will be solved to demonstrate the use of the design sensitivity analysis theory. The theory has also been discretized elsewhere using finite element approximations for implementation into structural analysis programs. These developments offer a firm foundation for design optimization of complex structural systems.

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

Keywords: Continuum formulation; geometric and material nonlinearities; Incremental nonlinear analysis; total Lagrangian concept; reference volume concept; shape and nonshape design problems

Citations: Zbl 0724.73159

Cited in: Zbl 0724.73159

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