Abstract
Optimization problems for plane-stress structures made of work-hardening elasto-plastic materials are theoretically considered. The deformation theory of plasticity is used. Optimality conditions for mean structural compliance minimization problems are obtained and investigated, and it is shown that the conditions lead to fully-stressed design. On the basis of the theoretical results obtained several optimization algorithms for the structures are developed. Numerical test results for the alogrithms are presented and analysed. High convergence rates of the algorithms are demonstrated. Significant physical properties of the numerical results are discussed.
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References
Arora, J.S.; Cardoso, J.E.B. 1989: A design sensitivity analysis and its implementation into ADINA.Comp. & Struct. 32, 691–705
Bendsøe, M.P.; Sokolowski, J. 1987: Sensitivity analysis and optimization of elastic-plastic structures.Eng. Opt. 11, 31–38
Cardoso, J.B.; Arora, J.S. 1988: Variational method for design sensitivity analysis in nonlinear structural mechanics.AIAA J. 26, 595–603
Choi, K.K.; Santos, J.L.T. 1987: Design sensitivity analysis of non-linear structural systems. Part I: theory.Int. J. Numer. Meth. Eng. 24, 2039–2055
Cinquini, C.; Contro, R. 1985: Optimal design of beams discretized by elastic-plastic finite element.Comp. & Struct. 20, 475–485
Cinquini, C.; Contro, R. 1987: Optimal design of elastic-plastic structures. In: Mota Soares C.A. (ed.)Computer aided optimal design: structural and mechanical systems, pp. 313–353. Berlin, Heidelberg, New York: Springer
Dems, K.; Mróz, Z. 1978: Multiparameter structural shape optimization by the finite element method.Int. J. Numer. Meth. Eng. 13, 247–266
Fleury, C. 1980: An efficient optimality criteria approach to the minimum weight design of elastic structures.Comp. & Struct. 11, 163–173
Ilyushin, A.A. 1948:Plasticity (in Russian). Moscow: Gostechteorizdat Publ.
Kachanov, L.M. 1969:Foundations of the theory of plasticity (in Russian). Moscow: Nauka
Kaneko, I.; Maier, G. 1981: Optimum design of plastic structures under displacement constraints.Comp. Meth. Appl. Mech. Eng. 27, 369–391
Komarov, A.A. 1965:Foundations of structural designing (in Russian). Kujbyshev: Kujbgosizdat Publ.
Mróz, Z.; Kamat, M.P.; Plaut, R.H. 1985: Sensitivity analysis and optimal design of nonlinear beams and plates.J. Struct. Mech. 13, 245–266
Nakamura, T.; Takewaki, I. 1989: Ductility design via optimum design of nonlinear elastic frames.J. Struct. Eng. 115, 608–625
Ryu, Y.S.; Haririan, M.; Wu, C.C.; Arora, J.S. 1985: Structural design sensitivity analysis of nonlinear response.Comp. & Struct. 21, 245–255
Saka, M.P. 1988: Optimum design of nonlinear space trusses.Comp. & Struct. 30, 545–551
Selyugin, S.V. 1992: Optimality criteria and algorithms for bar structures made of work-hardening elasto-plastic materials.Struct. Optim. 4, 218–223
Selyugin, S.V. 1994: On optimization of beams and frames made of work-hardening elasto-plastic materials.Struct. Optim. 7, 191–198
Tsay, J.J.; Arora, J.S. 1989: Optimum design of nonlinear structures with path dependent response.Struct. Optim. 1, 203–213
Tsay, J.J.; Arora, J.S. 1990: Nonlinear structural design sensitivity analysis for path dependent problems. Part 1: general theory.Comp. Meth. Appl. Mech. Eng. 81, 183–208
Tsay, J.J.; Cardoso, J.E.B.; Arora, J.S. 1990: Nonlinear structural design sensitivity analysis for path dependent problems. Part 2: analytical examples.Comp. Meth. Appl. Mech. Eng. 81, 209–228
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Communicated by A. Samsonov
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Selyugin, S.V. Optimality criteria-based algorithms for plane-stress elastoplastic structures. Structural Optimization 9, 207–213 (1995). https://doi.org/10.1007/BF01743971
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DOI: https://doi.org/10.1007/BF01743971