Shape sensitivity analysis for structural problems with non-linear material behaviour

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the "nite element method with a non-linear constitutive material model. Depending on the type of non-linear behaviour two di!erent 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 speci"c past time t6 (t6(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 di!erent examples