HIERARCHICAL MODELING OF THERMOELASTIC PLATES WITH VARIABLE THICKNESS

作者：Avalishvili G^*; Avalishvili M; Gordeziani D; Miara B

来源：Analysis and Applications, 2010, 8(2): 125-159.

DOI：10.1142/S0219530510001552

• Thermoelastic plates with variable thickness
• initial-boundary value problems
• Fourier-Legendre series
• modeling error estimates

The present paper is devoted to the construction and investigation of hierarchies of two-dimensional models for thermoelastic plates with variable thickness which may vanish on some part of the boundary. The hierarchical models are obtained by a semidiscretization of the three-dimensional problem in the transverse direction of plate. In suitable weighted Sobolev spaces, we prove existence and uniqueness of solutions of the initial-boundary value problems corresponding to the obtained two-dimensional models of thermoelastic plate with variable thickness. Moreover, we prove convergence in the corresponding spaces of the sequence of approximate solutions restored from the solutions of the reduced problems to the solution of the original three-dimensional problem and estimate the rate of convergence.

• 出版日期2010-4