Modal synthesis applied to a Reissner mixed plate finite element dynamic model
Résumé
This paper deals with the application of component mode synthesis on thick and thin plate finite element model, built with a Reissner mixed formulation. The Reissner mixed formulation is a structural mechanical formulation mostly used in plate problems that uses both displacement and generalized stress variables. Thus, the access to the stress in the plate is easier than with a primal method. The Mindlin theory for thick plates, permits to take into consideration shearing phenomenon inside the plate, whereas the Kirchoff-Love for thin plates only deals with bending and twisting phenomenons. The Reissner-mixed and primal models show the exact same results, both for Mindlin and Kirchoff-Love theory. Nevertheless, the Kirchoff-Love mixed model shows a much better convergence than the Mindlin mixed model for thick plates. The inconvenience of a mixed model, whatever the chosen plate theory is, is the numerical size of the finite element model that is much bigger. That's the reason why we use modal synthesis to reduce our model. The idea is to build our model with both primal and mixed formulation at the same time. Then we reduce the mixed model using a sub-structuring method and bases composed of "fixed interface modes" obtained from a Craig & Bampton method applied on the primal model. That method also shows a good convergence and permits us to reduce significantly the numerical size of our model on a certain frequency band, keeping the advantages of the Reissner mixed model.
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GARAMBOIS_Eurodyn_2014_Modal_synthesis_applied_to_a_Reissner_mixed_plate_finite_element_dynamic_model.pdf (1.24 Mo)
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