Enabling the analysis of finite element simulation bundles

Abstract

We propose a methodology capable of allowing a fast evaluation of thousands of finite element design variants simultaneously. This approach uses a high dimensional analysis concept, namely diffusion maps, that has been in use successfully for years in many areas of science. Using feature vectors from a bundle of finite element simulations containing information on the design variables on different mesh sizes and applying this analysis concept is the purpose of this paper. Applying this approach enables the identification of a set of parameters (reduction coordinates) along which (i) geometrical variants can be identified and (ii) for random time-dependent problems, slow variables can be identified that show the variables with the most significant impact on a design. We demonstrate the application of this approach in several industrial examples in the areas of metal forming and vibration analysis as well as vehicle crash simulation, which is a noisy stochastic process. Finally, we show per example that this approach can identify and expound on the occurrence of a bifurcation point, a very important issue in vehicle design.