## 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 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 ${\displaystyle t^{u}(t^{u}. 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.

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### Document information

Published on 01/01/1999

DOI: 10.1002/(SICI)1097-0207(19991130)46:9<1385::AID-NME704>3.0.CO;2-G