ALTERNATIVE MASS MATRICES AND INERTIA PATCH TESTS

Abstract eng:
Recent interest in alternative mass matrices emanates from explicit dynamics and impact/contact applications. Customized mass matrices may yield lower dispersion error for wave propagation problems [1]. Selective mass scaling techniques allow reduction of the computational costs for explicit finite element analyses [2] whereas singular mass matrices are used to reduce temporal oscillation of the contact forces in implicit computations [3]. For the derivation of such matrices a simple and fast consistency test, like the patch test for linear elastic problems, would be benificial. In this context, an inertia patch test was proposed in [4] and tested for several mass matrices and elements. In this talk, application of the inertia patch test is shown and the link between finite element technology for mass matrices and inertia patch test is discussed. The general aim of the underlying research is to advance construction of mass matrices to a level of maturity which has been achieved during the last decades for stiffness matrices in the context of finite element technology, for instance regarding locking and stability. In particular, the loading and the boundary conditions for several variants of the patch test, examples of failing the patch test, as well how partition of unity of certain quantities guarantees satisfaction of the patch test and the preservation of translational mass are presented. Moreover, the inertia patch test is extended to novel reciprocal mass matrices from [5].

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