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A new component mode synthesis for dynamic mixed thin plate finite element models

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Abstract

This paper presents a methodology for the reduction in dynamic mixed finite element models (DM-FEMs) based on the use of a sub-structuring primal methods adapted to such models. We implement a DM-FEM for Kirchhoff–Love thin plates using the Hellinger–Reissner variational mixed formulation adapted to dynamic, and give a quick insight of its convergence. This model uses both displacement and generalized stress fields within the plate, obtained as a primary result, but the numerical size of the model is bigger than with a primal displacement model. Thus, we choose to offset this complication by reducing the model with a totally new sub-structuring reduction method, especially adapted to DM-FEMs. The aim of our method is to adapt sub-structuring reduction methods commonly used for primal displacement FEM only (such as Craig and Bampton method) and split the reduction in the two fields. With these displacement methods, the whole structure is splitted into few smaller ones, and each of them is condensed with eigenmodes of the substructure and static connections between them. The principle of our method is to build, for each substructure, a reduced basis for the displacements according to the existing method, and a projection of the primal basis for the stresses. A new reduced basis for the whole mixed model is then built up exclusively with modes taken from the primal model. That method reduces significantly the number of degrees of freedom and keeps the properties and advantages of the mixed formulation.

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Acknowledgments

The first author gratefully acknowledges the French Education Ministry which supports this research.

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  1. LTDS, Ecole Centrale de Lyon, 36 av. Guy de Collongues, 69130, Ecully, France

    Pierre Garambois, Sébastien Besset & Louis Jézéquel

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  1. Pierre Garambois
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Garambois, P., Besset, S. & Jézéquel, L. A new component mode synthesis for dynamic mixed thin plate finite element models. Arch Appl Mech 86, 933–956 (2016). https://doi.org/10.1007/s00419-015-1072-x

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