Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity

1994/07/30 by Panagiotis Michaleris, Daniel A. Tortorelli, Creto A. Vidal +1 · 11 citations
Engineering · Materials Science · #Composite Structure Analysis and Optimization #Structural Behavior of Reinforced Concrete #Nonlocal and gradient elasticity in micro/nano structures

paper · doi:10.1002/nme.1620371408

Abstract

Abstract Tangent operators and design sensitivities are derived for transient non‐linear coupled problems. The solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods. The derived formulations are suitable for finite element implementations. Analyses of systems, with materials that exhibit history dependent response, may be obtained directly by applying the analyses of transient non‐linear coupled systems. Rate‐independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes.

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