From package and design surfaces to optimization - how to apply shape optimization under geometrical constraints

Abstract

During the product development process, the engineer needs to design mechanical structures regarding package and design surface restrictions. Accordingly, the use of package definitions and design surfaces results in a constraining volume. Shape optimization algorithms can be applied for component or assembly optimization. By variation and setting of the upper and lower boundaries, the shape of the optimized part is restricted. The optimization result needs to stay within this design space. Hence, the engineer or designer sets the design variables in such a way, that none of the created designs reaches beyond the design variable boundaries. This manual method is not able to prevent every infeasible design, due to the vast amount of possible designs in the solution space. As well, the effort to set the design variables by hand is high for the designer. To avoid this manual and vulnerable process, the authors introduced and implemented a method for the automated detection of geometric infeasibility. The process is also named optimization under geometric infeasibility.This paper applies this method to a more complex example, which includes the detection of complex constraining geometries. It demonstrates the benefits of the method and how it can be applied in the product development process. Therefore, a generic b-pillar has been designed in SFE CONCEPT. The structural performance of this b-pillar is thought to be increased by a shape optimization. From a literature review, the dimensions of a parametric package and design surface are derived. In-between the surface definition, the algorithm creates feasible designs. Penalized designs are detected if a surface penetration of the assembly/component and the enveloping surface takes place. Hence, this method enables the optimization of structural performance with an NSGA-II, while the designs are geometrically feasible. Besides the validation of the method for population-based algorithms, this paper introduces and discusses the use of surrogate models for optimization under the geometrical constraint.