engleski

Evolution Model for Linearized Micropolar Plates by the Fourier Method

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.

micropolar elasticity; asymptotic analysis; plate model; the Fourier method

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