Nested loop approach for topology and shape optimization of crash-loaded deep-drawn components using contact forces for the inner loops

Abstract

In this paper a new method for the optimization of deep-drawn shell components in crash by using substitute load cases in established sensitivity based static optimization is presented. The optimization process is split into an inner and an outer loop. In the outer loop the contact forces during crash are determined. These contact forces are used as substitute load cases in a static topology optimization, which builds the inner loop of the method. The presented method was inspired by the Equivalent Static Loads Method, but differs primarily in two aspects. These are the use of the contact forces as alternative to equivalent static loads in the linear static topology optimization and the extraction of a shell model that represents the voxel result obtained from topology optimization. A manufacturing constraint is applied in the topology optimization so that the results are shell components. This manufacturing constraint is enabling the mentioned extraction of a shell model. Two examples are presented where the method is applied to minimize the intrusion. The first example is a cantilever, the second example is a structure that is twisted. In both examples a rigid body impacts the structure. The method has shown to be numerical stable and suitable for the shown examples when the intrusion is the objective of the optimization. The intrusion was reduced significantly in both examples. The key novelty of the presented method is the ability to perform a static topology optimization of a voxel design space for a non-linear dynamic optimization model with the result being a shell model that can be analyzed for crash.