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 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 tu (tu<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