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Nonlinear structural design sensitivity analysis for path dependent problems. II: Analytical examples. (English) Zbl 0724.73159
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:
74P99Optimization in solid mechanics
74H45Vibrations (dynamical problems in solid mechanics)
74S05Finite element methods in solid mechanics