Component based model order reduction with mortar tied contact for nonlinear quasi-static mechanical problems

TL;DR

This paper introduces a component-based model order reduction method for nonlinear quasi-static mechanical problems, utilizing proper orthogonal decomposition and mortar-tied contact to efficiently simulate complex structures.

Contribution

The method combines component-wise POD reduction with mortar-tied contact formulation, enabling efficient and accurate reduced models for nonlinear structures with non-matching meshes.

Findings

Accurately predicts solutions not in the snapshot set.

Reduces computational effort through selective snapshot computation.

Effective for problems with material and geometric nonlinearity.

Abstract

In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a mortar-tied contact formulation. The snapshots for the substructure projection matrices are computed on the substructure level by the proper orthogonal decomposition (POD) method. The snapshots are computed using a random sampling procedure based on a parametrization of boundary conditions. To reduce the computational effort of the snapshot computation full-order simulations of the substructures are only computed when the error of the reduced solution is above a threshold. In numerical examples, we show the accuracy and efficiency of the method for nonlinear problems involving material and geometric nonlinearity as well as non-matching meshes. We are able to predict solutions of systems that we did not compute in our snapshots.