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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:

74P99 Optimization problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics

Citations:

Zbl 0724.73158

Software:

ADINA
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Full Text: DOI

References:

[1] Tsay, J. J.; Arora, J. S., Nonlinear structural design sensitivity analysis for path dependent problems. Part 1: General theory, Comput. Methods Appl. Mech. Engrg., 81, 183-208 (1990) · Zbl 0724.73158
[2] Cardoso, J. E.B.; Arora, J. S., Design sensitivity analysis and optimization of nonlinear structures: A unified approach, (Technical Report No. ODL-88.3 (1988), Optimal Design Laboratory, College of Engineering, The University of Iowa: Optimal Design Laboratory, College of Engineering, The University of Iowa Iowa City, IA), (available at NTIS, No. PB88-23517/A11) · Zbl 0705.73208
[3] Arora, J. S.; Cardoso, J. E.B., A design sensitivity analysis principle and its implementation into ADINA, Comput. & Structures, 32, 3/4, 691-705 (1989) · Zbl 0705.73208
[4] Tsay, J. J.; Arora, J. S., Design sensitivity analysis of nonlinear structures with history dependent effects, (Technical Report No. 88.4 (1988), Optimal Design Laboratory, The University of Iowa, College of Engineering: Optimal Design Laboratory, The University of Iowa, College of Engineering Iowa City, IA 52242 U.S.A) · Zbl 0724.73158
[5] Tsay, J. J.; Arora, J. S., Variational methods for design sensitivity analysis of nonlinear response with history dependent effects, (International Conference on Computational Engineering Science. International Conference on Computational Engineering Science, Atlanta, GA, U.S.A. (1988), Springer: Springer New York), 45.vii
[6] Tsay, J. J.; Arora, J. S., Optimum design of nonlinear structures with path dependent response, Structural Optimization, 1, 4, 203-214 (1989)
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