Inverse Thermoelastic Analysis of a Thick Rectangular Plate

Thermal stresses and displacement functions are obtained for a rectangular plate occupying the space R: -a < x < a, 0 < y < b, -h < z < h, with the known boundary and initial conditions. In this inverse problem the unknown surface temperature is determined on the boundary along the y-axis when the temperature at some internal point is known. The governing heat conduction equation has been solved by applying Marchi – Fasulo transform and Laplace transform techniques. The solutions are obtained in form of infinite series. The results for displacement and thermal stresses have been computed numerically and illustrated graphically for Aluminium plate. MSC 2010: 74A10,74J25, 74H99, 74D99

Solving the Deflection Equations of Thick Plate under Concentrated Load

According to reciprocal-theorem method (RTM), the deflection equations of thick rectangular plate with two edges simply supported and two edges free under concentrated load are obtained in this paper. Simultaneously through the programming computation, the numerical results with actual value are obtained, which further showed the accuracy and superiority of RTM to solve the bending of thick rectangular plates.

On the Applicability of New Symplectic Approach for Exact Bending Solutions of Moderately Thick Rectangular Plate

The exact bending solutions of moderately thick rectangular plates with two opposite sides simply supported are derived based on the symplectic geometry method. The basic equations for the plates are transferred into Hamilton canonical equations. Then the whole state variables are separated. According to the method of eigenfunction expansion in the symplectic geometry, the exact bending solutions of the plates are obtained. Since only the basic elasticity equations of the plates are used and there is no need to select the deformation functions arbitrarily, the approach utilized is completely reasonable.

Bending of Thick Rectangular Plates with Different Boundaries under Concentrated Load

Reciprocal theorem method (RTM) is generalized to solve the problem of bending of thick rectangular plate under concentrated load with four edges fixed and with two opposite edges fixed, the third edge simply supported, and the fourth edge free based on Reissner’s theory. The analytical solutions of the thick plate are given, and the relevant date and diagram are given to guidance engineering application.