Spline-based shape optimization of large-scale composite leaf spring models using Bayesian strategies with multiple constraints

The presented paper describes a shape optimization workflow using Bayesian strategies. It is applied to a novel automotive axle system consisting of leaf springs made from glass fiber reinforced plastics (GFRP). Besides the primary objectives of cost and mass reduction, the assembly has to meet multiple technical constraints with respect to various loading conditions. The related large-scale finite element model is fully parameterized by splines, hence the general shape of the guide curve as well as the spring’s height, width and material properties can be altered by the corresponding workflow. For this purpose, a novel method is developed to automatically generate high-quality meshes depending on the geometry of the respective springs. The size and complexity of the model demands the implementation of efficient optimization techniques with a preferably small number of required response function evaluations. Therefore, an existing optimization framework is extended by state-of-the-art Bayesian methods, including different kernel combinations and multiple acquisition function approaches, which are then tested, evaluated and compared. To properly address the use of GFRP as spring material in the objective function, an appropriate cost model is derived. Emerging challenges, such as conflicting targets regarding direct material costs and potential lightweight measures, are considered and investigated. The intermediate steps of the developed optimization procedure are tested on various sample functions and simplified models. The entire workflow is finally applied to the complete model and evaluated. Concluding, ideas and possibilities in improving the optimization process, such as the use of models with varying complexity, are discussed.