Nonparametric gradient-less shape optimization for real-world applications

A nonparametric gradient-less shape optimization approach for finite element stress minimization problems is presented. The shape optimization algorithm is based on optimality criteria, which leads to a robust and fast convergence independent of the number of design variables. Sensitivity information of the objective function and constraints are not required, which results in superior performance and offers the possibility to solve the structural analysis task using fast and reliable industry standard finite element solvers such as ABAQUS, ANSYS, I-DEAS, MARC, NASTRAN or PERMAS. The approach has been successfully extended to complex nonlinear problems including material, boundary and geometric nonlinear behavior. The nonparametric geometry representation creates a complete design space for the optimization problem, which includes all possible solutions for the finite element discretization. The approach is available within the optimization system TOSCA and has been used successfully for real-world optimization problems in industry for several years. The approach is compared to other approaches and the benefits and restrictions are highlighted. Several academic and real-world examples are presented.