2. Basic principles of topological optimization in mechanics

We are considering a discretization using the finite element method is used for discretization, and to simplify, in linear elasticity, which is most often the case in topological optimization, at least for initial design purposes. We denote U the generalized displacement vector, which must respect boundary conditions, K the stiffness matrix and F the generalized force vector. The equilibrium and boundary conditions of the problem are expressed by the system :