Abstract
Nowadays, product development times are constantly decreasing, while the requirements for the products themselves increased significantly in the last decade. Hence, manufacturers use Computer-Aided Design (CAD) and Finite-Element (FE) Methods to develop better products in shorter times. Shape optimization offers great potential to improve many high-fidelity, numerical problems such as the crash performance of cars. Still, the proper selection of optimization algorithms provides a great potential to increase the speed of the optimization time. This article reviews the optimization performance of two different algorithms and frameworks for the structural behavior of a b-pillar. A b-pillar is the structural component between a car’s front and rear door, loaded under static and crash requirements. Furthermore, the validation of the algorithm includes a feasibility constraint. Recently, an optimization routine was implemented and validated for a Non-dominated Sorting Genetic Algorithm (NSGA-II) implementation. Different multi-objective optimization algorithms are reviewed and methodically ranked in a comparative study by given criteria. In this case, the Gap Optimized Multi-Objective Optimization using Response Surfaces (GOMORS) framework is chosen and implemented into the existing Institut für Konstruktionstechnik Optimizes Shapes (IKOS) framework. Specifically, the article compares the NSGA-II and GOMORS directly for a linear, non-linear, and feasibility optimization scenario. The results show that the GOMORS outperforms the NSGA-II vastly regarding the number of function calls and Pareto-efficient results without the feasibility constraint. The problem is reformulated to an unconstrained, three-objective optimization problem to analyze the influence of the constraint. The constrained and unconstrained approaches show equal performance for the given scenarios. Accordingly, the authors provide a clear recommendation towards the surrogate-based GOMORS for costly and multi-objective evaluations. Furthermore, the algorithm can handle the feasibility constraint properly when formulated as an objective function and as a constraint.
Highlights
A common way to save weight in structural design is to use optimization approaches in the product development process (PDP) [1,2], such as topology, shape, and size optimization
The design space, representing the external geometric constraint from package and design, is highlighted in red. Another problem is the ratio of infeasible designs by the intersecting hull surface, which reduces the number of calculated designs [18,20]
Approximately 200 members are calculated during the optimization; still, the number of design variables is increased by two, which increases the size of the solution space
Summary
A common way to save weight in structural design is to use optimization approaches in the product development process (PDP) [1,2], such as topology, shape, and size optimization. Engineers apply the mentioned optimization types in different stages of the PDP, for instance, the preliminary or conceptual design. Engineers mostly use shape optimization in all design-relevant stages of the PDP. In automotive design, complex structures with multiple requirements exist, with crash safety being the most challenging. Due to decreasing computational cost, crash calculations are state of the art in the automotive design process regarding the dimensioning of structural components. The potential of automotive BIW crash optimization strongly depends on optimization algorithms that precisely find a good design by using a minimum of the expensive function evaluations. Good designs in a crash are lightweight and fulfill all requirements towards crash safety, package, and structural stiffness [5,6,7]
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