Model Order Reduction for Parametric Nonlinear Mechanical Systems - State-of-the-Art and Future Research

Finite-element-analyses of advanced mechanical structures that undergo large deflections usually lead to high-dimensional systems of nonlinear equations. Their solution requires high computational effort which is crucial for design iterations, such as optimization or parameter studies. Nonlinear model order reduction methods are used to reduce these computational costs. Similar to reduction methods for linear systems, the number of unknowns is reduced by projecting the displacements onto a subspace spanned by a reduction basis. In contrast to linear systems, nonlinear systems do not have eigenvectors which can be used as reduction basis. For developing nonlinear reduction methods, it is a first challenge to determine a good reduction basis that is small but accurate. A second challenge is to reduce computational costs for the evaluation of the nonlinear term. While in linear analyses the stiffness matrix can be simply reduced by matrix multiplications, in nonlinear analysis the nonlinear force vector has to be evaluated at every iteration step in the full element domain. In order to reduce these evaluation costs, hyperreduction methods are used. This contribution gives an overview of state-of-the-art-methods for both basis-selection and hyperreduction. Furthermore, we give an outlook on our future research within our project in the DFG Priority Program 1897 "Calm, Smooth and Smart Structures". It deals with the development of simulation-free hyperreduction techniques for parametric nonlinear mechanical systems.      «

Finite-element-analyses of advanced mechanical structures that undergo large deflections usually lead to high-dimensional systems of nonlinear equations. Their solution requires high computational effort which is crucial for design iterations, such as optimization or parameter studies. Nonlinear model order reduction methods are used to reduce these computational costs. Similar to reduction methods for linear systems, the number of unknowns is reduced by projecting the displacements onto a su...     »