"Proper Orthogonal Decomposition for Model-Order Reduction of Nonlinear Mechanical Systems"
Proper Orthogonal Decomposition for Model-Order Reduction of Nonlinear Mechanical Systems
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In recent years finite element models and multi-body systems in solid mechanics have been becoming more and more complex. Coupling problems from different fields may further increase the computational complexity. In this master thesis the proper orthogonal decomposition, a model-order reduction method, is applied to mechanical systems. The goal is to reduce the number of equations which have to be solved without sacrificing accuracy. The method described in this work uses data from the original model to create a lower-dimensional subspace. With the aid of projection methods, the full system is projected onto the subspace. The approach promises that the subspace includes the most relevant parts of the original model. Special focus lies on an estimation of the dimension of the transformation bases. In order to provide an overview of how the reduction method works on mechanical problems, various finite element models have been set up. A linear dynamic calculation of a two-dimensional structure is performed and results are given. Applying the proper orthogonal decomposition method on nonlinear systems, the complexity of evaluating the nonlinear part still remains of the dimension of the full system. The discrete empirical interpolation method is introduced to avoid evaluations of full-dimensional terms. To get a deeper insight into the methods, several parameter variations are performed and issues like numerical stability are addressed. To solve time-dependent problems, three time-integration methods in connection with the model order reduction are investigated. Concepts and possible tasks for future work are presented, including modifications of the proper orthogonal decomposition method and the discrete empirical interpolation method.