Design sensitivity analysis of elastic-plastic analysis problems

ABSTRACT Elastic-plastic analysis problems are formulated as quadratic programming problems that involve energy functionals and equilibrium and yield constraints that depend on the design, material, and loading. The paper considers the problem of determining the variation in structural response, due to variations of these parameters. A general result is obtained for discrete structures. As an example of a distributed structure, a statically determinate beam that is described by a model in two spatial variables is considered. Implications for optimal design are also discussed and the sensitivity result is employed in the solution procedure for an optimization problem for a simple truss-structure under elastoplastic deformation.

[1]  K. Jittorntrum.  Solution point differentiability without strict complementarity in nonlinear programming , 1984 .

[2]  R. Tobin.  Sensitivity analysis for variational inequalities , 1986 .

[3]  J. Sokołowski.  Sensitivity Analysis for a Class of Variational Inequalities , 1981 .

[4]  Kazimierz Malanowski.  Differentiability with respect to parameters of solutions to convex programming problems , 1985, Math. Program..

[5]  Björn Birnir,et al.  Complex hill's equation and the complex periodic korteweg‐de vries equations , 1986 .

[6]  Roberto Contro,et al.  Optimal design of beams discretized by elastic plastic finite element , 1985 .

[7]  G. Maier.  A matrix structural theory of piecewise linear elastoplasticity with interacting yield planes , 1970 .

[8]  Moshe F. Rubinstein,et al.  Elastic-Plastic Analysis by Quadratic Programming , 1972 .

[9]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[10]  D. E. Grierson,et al.  Mathematical programming and nonlinear finite element analysis , 1979 .

[11]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[12]  Giulio Maier,et al.  Optimum design of plastic structures under displacement constraints , 1981 .

[13]  Claes Johnson,et al.  On plasticity with hardening , 1978 .

[14]  M. Z. Cohn,et al.  Engineering Plasticity by Mathematical Programming , 1981 .

[15]  Martin P. Bendsae,et al.  Sensitivity Analysis of Problems of Elasticity with Unilateral Constraints , 1985 .

[16]  R. Mifflin.  Semismooth and Semiconvex Functions in Constrained Optimization , 1977 .

[17]  R. Kohn,et al.  Optimal design and relaxation of variational problems, III , 1986 .