Model Order Reduction for Nonlinear Modular Structures by Hyperreduction of the Components and Mortar Tied Contact
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Many structures are composed of components that are assembled into a global structure. For linear structures of this type, there exist widespread methods to build a reduced order model such as the Craig-Bampton methods or other component mode synthesis methods. It is still an open question how to extend these methods for nonlinear mechanics. In this work, we propose a model order reduction (MOR) method where the components are reduced individually and are connected by a mortar tied contact formulation. Our MOR method consists of two parts. The first part is the hyperreduction of the substructures, where we use energy conserving sampling and weighting (ECSW) with a projection matrix computed by proper orthogonal decomposition (POD).The POD basis of each substructure is precomputed from representative deformation states. The second part is the connection of the components to form a global system. Here we use a mortar tied contact formulation, which enables us to connect components with non-matching meshes. A further advantage is that the Lagrange multipliers can be removed from the equation system by static condensation, by choosing dual shape functions for the Lagrange multipliers. We apply the method for quasistatic solid mechanics problems with finite deformations and nonlinear material behavior.
