Published in Structural Optimization Vol. 17 (2-3), pp. 162-171, 1999
DOI: 10.1007/BF01195941

Abstract

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past time$t^{u}(t^{u}<t)$. This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening.

For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some examples.

J. Kato, A. Lipka, E. Ramm. Multiphase material optimization for fiber reinforced composites with strain softening. Struct Multidisc Optim 39(1) (2008) DOI 10.1007/s00158-008-0315-7

J. Kato, H. Hoshiba, S. Takase, K. Terada, T. Kyoya. Analytical sensitivity in topology optimization for elastoplastic composites. Struct Multidisc Optim 52(3) (2015) DOI 10.1007/s00158-015-1246-8

S. Schwarz, E. Ramm. Sensitivity analysis and optimization for non‐linear structural response. Engineering Computations 18(3/4) DOI 10.1108/02644400110387181

J. KATO, E. RAMM, K. TERADA, T. KYOYA. MULTIPHASE MATERIAL OPTIMIZATION FOR FIBER REINFORCED COMPOSITES CONSIDERING STRAIN SOFTENING. J. JSCE 67(1) DOI 10.2208/jscejam.67.39

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