Chapter41 DEIM for the Efficient Computation of Contact Interface Stresses M. Breitfuss, H. Irschik, H.J. Holl and W. Witteveen Abstract The computational effort for the simulation of reduced order models containing contact stresses is determined by these nonlinear terms. Recent publications suggest the utilization of interpolation methods to overcome this bottleneck. The applicability of the Discrete Empirical Interpolation Method (DEIM) for the efficient computation of contact stresses is demonstrated. The modeling of a mechanical structure containing an interface using zero thickness elements is outlined first. This is followed by a reduction method using joint interface modes as extension to the well known Craig Bampton approach. The basic idea of interpolation methods and a summary of the applied DEIM algorithm is given. Finally the numerical example of a bolted cantilever is investigated for two loadcases and the results are discussed for different trial function bases. It is clearly shown that DEIM can be used to significantly improve the computational efficiency for this type of problems while keeping accuracy at an acceptable level. Keywords DEIM • POD • Model Order Reduction • Joint Contact Consideration • Interpolation Method 41.1 Introduction This contribution focuses on the efficient consideration of contact stresses within the framework of reduced order models for mechanical systems. Literature and current investigations of the authors clearly point out that the computational effort for the simulation of reduced order models containing contact stresses is determined by these nonlinear terms as the evaluation still takes place on the discretization of the full model. Furthermore a coordinate transformation from generalized coordinates to physical coordinates and the projection of the resulting stresses onto the generalized coordinates is necessary, which leads to an even higher computational effort involved for the interface stress computation compared to the full model. Interpolation methods are an effective approach to lower the computational effort involved with the evaluation of parametrized functions defined on a spatial domain [6]. Furthermore in [2] the Discrete Empirical Interpolation Method (DEIM) is suggested to lower the computational effort for reduced order models containing nonlinear functions. In this case the former mentioned transformation and projection is only necessary for some few physical coordinates. The scaling of the interpolation functions is determined by collocation of function values and interpolated values at these so called interpolation points. To demonstrate the applicability of DEIM for efficient computation of joint interface stresses the problem is formulated as single body involving self contact. The theory of zero thickness elements, see [4] and [5], is used to discretize the joint contact. The authors suggest a zero thickness element formulation leading to a contact stress equivalent force vector. This allows for a model order reduction following [3, 8] and fits into the DEIM formulation proposed by [2]. M. Breitfuss ( ) • H. Irschik • H.J. Holl Johannes Kepler University Linz, Altenbergerstr. 69, 4040 Linz, Austria e-mail: markus.breitfuss@jku.at W. Witteveen University of applied sciences Wels, Stelzhamerstr. 23, 4600 Wels, Austria M. Allen et al. (eds.), Dynamics of Coupled Structures, Volume 1: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04501-6__41, © The Society for Experimental Mechanics, Inc. 2014 435
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