Accelerated non‐linear stability analysis based on predictions from data‐based surrogate models

Abstract

In many applications in computer‐aided engineering, like parametric studies, structural optimization, or virtual material design, a large number of almost similar models must be simulated. Although the individual scenarios may differ only marginally in both space and time, the same amount of effort is invested in each new simulation, without taking into account the experience and knowledge gained in previous simulations. Therefore, we have developed a method that combines data‐based Model Order Reduction (MOR) and reanalysis, exploiting knowledge from previous simulation runs to accelerate computations in multi‐query contexts. While MOR allows reducing model fidelity in space and time without significantly deteriorating accuracy, reanalysis uses results from previous computations as a predictor or preconditioner. In particular, this method enables acceleration of the exact computation of critical points, such as limit and bifurcation points, by the method of extended systems for systems that depend on a set of design parameters, such as material or geometric properties. Such critical points are of utmost engineering significance due to the special characteristics of the structural behavior in their vicinity. Conventional reanalysis methods, like the fold line analysis, can be used to accelerate the computation of critical points of almost similar systems but are limited in their applicability. For the fold line analysis, only small parameter variations are possible as the algorithm may not converge to the correct solution or fail to converge elsewise. Moreover, this method is only suited to finding the first critical points of limit point problems. In contrast to that, our developed data‐based “reduced model reanalysis” method overcomes these problems. Thus, a larger parameter space can be covered. The efficiency of this method is demonstrated for a couple of numerical examples, including standard and isogeometric finite element models.