Optimization and Identification of the Shape in Elastoplastic Boundary Problems Using Parametric Integral Equation System (PIES)

The paper presents optimization and identification of the shape of elastoplastic structures. The optimization process is performed by the particle swarm method (PSO), while direct boundary value problems are solved using the parametric integral equation system (PIES). Modeling the boundary and the plastic zone in PIES is done globally by the small number of control points of parametric curves and surfaces. Such way of defining is very beneficial in comparison to so-called element methods (finite or boundary), because it reduces the number of design variables and does not enforce re-discretization during each shape change. Together with advantages of PSO it is an effective approach to solving optimization problems. There are three examples in the paper: two of identification of the shape and one in which an optimal shape is searched.