Optimal design of shells with FE based parameterization

In a finite element (FE) based parameterization, data of the FE mesh are used as design variables, such as nodal coordinates and nodal thickness. During shape and thickness optimization, this approach provides much design freedom for a limited modeling effort. Stress results are, however, very sensitive to the local shape changes that can occur during FE based optimization. When stress results are used as response function, this irregularity can complicate the optimization. As a solution, the KreisselmeierSteinhauser function for the stresses is introduced as a response function for FE based optimization. In this function, the local stress results are aggregated to obtain a global measure of stress in a structure. This measure can be used as an objective to reduce the overall stress in the structure or as a constraint to limit the stress in the structure to a maximum allowable value. As a result, the optimal structures are smooth and material efficient. Several examples are presented in this paper to illustrate the use of the FE based design approach in combination with the stress response function. Keywords— shape and size optimization, parameter free optimization, shell structures