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Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity
Author(s) -
Michaleris Panagiotis,
Tortorelli Daniel A.,
Vidal Creto A.
Publication year - 1994
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620371408
Subject(s) - tangent , sensitivity (control systems) , transient (computer programming) , mathematics , finite element method , transient response , linear system , mathematical analysis , mathematical optimization , computer science , engineering , geometry , structural engineering , electronic engineering , electrical engineering , operating system
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.