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Local and global strategies for optimal selective mass scaling

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Abstract

The problem of optimal selective mass scaling for linearized elasto-dynamics is discussed. Optimal selective mass scaling should provide solutions for dynamical problems that are close to the ones obtained with a lumped mass matrix, but at much smaller computational costs. It should be equally applicable to all structurally relevant load cases. The three main optimality criteria, namely eigenmode preservation, small number of non-zero entries and good conditioning of the mass matrix are explicitly formulated in the article. An example of optimal mass scaling which relies on redistribution of mass on a global system level is constructed. Alternative local mass scaling strategies are proposed and compared with existing methods using one modal and two transient numerical examples.

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Notes

  1. Independently published and analyzed for linear and non-linear problems in [10].

  2. The Jacobi preconditioner contains on the diagonal the inverted values of \({\mathbf {{P}}}_{\mathrm {J},ii } = ({\mathbf {{M}}}_{ii})^{-1}\).

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Acknowledgments

The authors are thankful to both reviewers for their detailed and helpful comments which significantly improved the manuscript. Moreover, the helpful discussions with our graduate student Baris Cansiz in the primary stage of this work are gratefully acknowledged.

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  1. Institut für Baustatik und Baudynamik, Universität Stuttgart, Pfaffenwaldring 7, 70550 , Stuttgart, Germany

    Anton Tkachuk & Manfred Bischoff

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  1. Anton Tkachuk
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  2. Manfred Bischoff
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Correspondence to Anton Tkachuk.

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Support of Baden-Württemberg Stiftung gGmbH Grant HPC-10 is gratefully acknowledged.

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Tkachuk, A., Bischoff, M. Local and global strategies for optimal selective mass scaling. Comput Mech 53, 1197–1207 (2014). https://doi.org/10.1007/s00466-013-0961-5

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