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Shape sensitivity analysis for structural problems with non‐linear material behaviour
Author(s) -
Bugeda Gabriel,
Gil Lluís
Publication year - 1999
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/(sici)1097-0207(19991130)46:9<1385::aid-nme704>3.0.co;2-g
Subject(s) - plasticity , linear elasticity , finite element method , sensitivity (control systems) , constitutive equation , mathematics , elasticity (physics) , softening , reliability (semiconductor) , computer science , structural engineering , engineering , materials science , physics , statistics , electronic engineering , composite material , power (physics) , quantum mechanics
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 non‐linear constitutive material model. Depending on the type of non‐linear behaviour two different approaches are proposed. First, a new direct (non‐incremental) formulation is proposed for material models characterized by the fact that the stresses at any time t can be expressed in terms of the strains at the same time t 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 non‐linear), perfect plasticity and damage models. Second, a more classical incremental approach is proposed for general plasticity cases. A special strategy is also proposed for material models with strain softening. The quality and reliability of the proposed approaches are assessed through their application in different examples. Copyright © 1999 John Wiley & Sons, Ltd.