Adjoint Structure Approach for Shape‐Sensitivity Analysis using BEM
Publication: Journal of Engineering Mechanics
Volume 116, Issue 12
Abstract
An adjoint approach for the shape design sensitivity analysis of plane elasticity problems with a direct boundary integral equation formulation is presented. The objective function or the constraint function is expressed in an integral form and augmented by incorporating the elasticity equations via adjoint functions. The variation of the augmented function is taken by performing its material derivative to obtain the sensitivity of the objective function or the constraint function. The adjoint functions are obtained through the solution of the adjoint problem resulting from setting the local variations of the displacement, velocity, and traction fields equal to zero. An approximate procedure for the application of concentrated adjoint load in the boundary element framework is suggested. This allows the computation of displacement, traction, and stress sensitivities at discrete nodal points. The requirement of choosing an averaging characteristic function in earlier formulations is obviated by this development. The present formulation includes the treatment of body forces in sensitivity calculations. A series of numerical examples is solved to demonstrate the validity of the present approach.
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References
1.
Adelman, H. M., and Haftka, R. T. (1986). “Sensitivity analysis of discrete structural systems.” AIAA J., 24(5), 823–832.
2.
Aithal, R., Saigal, S., and Mukherjee, S. (1990). “Three dimensional boundary element implicit differentiation formulation for design sensitivity analysis.” Computers and Mathematics with Applications, Pergamon Press, Elmsford, N.Y.
3.
Banerjee, P. K., and Butterfield, R. (1981). Boundary element methods in engineering science. McGraw‐Hill Book Co., London, United Kingdom.
4.
Banerjee, P. K., Ahmad, S., and Chen, K. (1988). “Application of BEM to wave barriers in multi‐layered three‐dimensional soil media.” Earthquake Engrg. and Struct. Dynamics, 16, 1041–1060.
5.
Barone, M., and Yang, R. J. (1988). “Boundary integral equations for recovery of design sensitivities in shape optimization.” AIAA J., 26, 589–594.
6.
Bennett, J. A., and Botkin, M. E. (1986). The optimum shape: Automated structural design, Plenum Press, New York, N.Y.
7.
Choi, J. H., and Kwak, B. M. (1988). “Boundary integral equation method for shape optimization of elastic structures.” Int. J. Num. Meth. Engrg., 26, 1579–1595.
8.
Dems, K., and Mroz, Z. (1984). “Variational approach by means of adjoint systems to structural optimization and sensitivity analysis II, structure shape variation.” Int. J. Solids Struct., 20(6), 527–552.
9.
Haug, E. J., Choi, K. K., and Komkov, V. (1986). Design sensitivity analysis of structural systems. Academic Press, New York, N.Y.
10.
Kane, J. H., and Saigal, S. (1988). “Design sensitivity analysis of solids using BEM.” J. Engrg. Mech., ASCE, 114(10), 1703–1722.
11.
Meric, R. A. (1984). “Boundary elements for static heating of solids.” J. Heat Transfer, 106, 876–880.
12.
Meric, R. A. (1988). “Shape design sensitivity analysis of dynamic structures.” AIAA J., 26(2), 206–212.
13.
Mota Soares, C. A., and Choi, K. K. (1986). “Boundary elements in shape optimal design of structures.” The Optimum Shape: Automated Structural Design, J. A. Bennett and M. E. Botkin, eds., Plenum Press, New York, N.Y., 199–231.
14.
Mukherjee, S. (1982). Boundary element methods in creep and fracture. Elsevier Applied Science, London, United Kingdom.
15.
Mukherjee, S., and Chandra, A. (1969). “A boundary element formulation for design sensitivities in materially nonlinear problems.” Acta Mechanica, 78, 243–253.
16.
Mukherjee, S., and Chandra, A. (1990). “A boundary element formulation for design sensitivities in problems involving both geometric and material nonlinearities.” Computers and Mathematics with Applications (in press).
17.
Mushkhelishvili, N. I. (1963). Some basic problems of the mathematical theory of elasticity. P. Noordhoff Ltd., Groningen, The Netherlands.
18.
Pape, D. A., and Banerjee, P. K. (1987). “Treatment of body forces in 2D elastostatics BEM using particular integrals.” J. Appl. Mech., 54, 866–871.
19.
Park, C. W., and Yoo, Y. M. (1988). “Shape design sensitivity analysis for a two‐dimensional heat transfer system using the boundary element method.” Comp. Struct., 28, 543–550.
20.
Rice, J. S., and Mukherjee, S. (1990). “Design sensitivity coefficients for axisymmetric elasticity problems by boundary element methods.” Engineering Analysis, Computational Mechanics Publications, Southampton, United Kingdom.
21.
Saigal, S., Borggaard, J. T., and Kane, J. H. (1989). “Boundary element implicit differentiation equations for design sensitivities of axisymmetric structures.” Int. J. Solids Struct., 25(4–6), 527–538.
22.
Saigal, S., and Chandra, A. (1990). “Shape sensitivities and optimal configurations for heat diffusion problems.” ASME J. Heat Transfer (in press).
23.
Wu, S. J. (1986). “Applications of the boundary element method for structural shape optimization,” thesis presented to the University of Missouri, at Columbia, Mo., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
24.
Yang, R. J., and Botkin, M. E. (1986). “Comparison between the variational and implicit differentiation approaches to shape design sensitivities.” AIAA J., 24(6), 1027–1032.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 116 • Issue 12 • December 1990
Pages: 2663 - 2680
Copyright
Copyright © 1990 ASCE.
History
Published online: Dec 1, 1990
Published in print: Dec 1990
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