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Evolution Model for Linearized Micropolar Plates by the Fourier Method

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Abstract

In this paper we justify a two-dimensional evolution and eigenvalue model for micropolar plates starting from three-dimensional linearly micropolar elasticity. A small parameter representing the thickness of the plate-like body is introduced in the problem. The asymptotics of the evolution and eigenvalue problems is then developed as this small parameter tends to zero. First the appropriate convergences of the eigenpairs of the three-dimensional problem to the eigenpairs of the two-dimensional eigenvalue problem for micropolar plates is shown. Then these convergences are used in the Fourier method to obtain the convergences of the solution of the three-dimensional evolution problem to the solution of the two-dimensional evolution plate model.

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, 10000, Zagreb, Croatia

    Josip Tambača & Igor Velčić

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  1. Josip Tambača
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  2. Igor Velčić
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Correspondence to Josip Tambača.

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Tambača, J., Velčić, I. Evolution Model for Linearized Micropolar Plates by the Fourier Method. J Elasticity 96, 129–154 (2009). https://doi.org/10.1007/s10659-009-9202-8

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  • DOI: https://doi.org/10.1007/s10659-009-9202-8

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