Maximum energy dissipation for elasto-plastic plates via isogeometric shape optimization

In this research, optimum shape of plate structures is sought to maximize the energy dissipation via structural shape optimization. To achieve this, isogeometric analysis (IGA) is utilized for structural analysis of plates considering elasto-plastic behavior of materials. The von Mises material model is employed for this purpose. Non-uniform rational B-splines basis functions are used for both geometry definition and approximating the unknown deformation field. The optimization problem is to maximize the structural dissipated energy until a prescribed displacement is reached and a fixed amount of material is considered in the design domain. A direct shape sensitivity analysis is performed and a mathematical based approach is employed for the optimization process. To demonstrate the efficiency of the proposed algorithm three examples are illustrated. Using the IGA prevents adjusting analysis model during the optimization process, which is time-consuming especially when iterative nonlinear analysis is performed. The results also show that large geometry modifications can be properly managed by the proposed algorithm.