Levy solution for thermal buckling analysis of thin functionally graded rectangular plates

In the present study, thermal buckling analysis of functionally graded (FG) rectangular plates with Levy boundary conditions is presented. Based on the classical plate theory, stability equations are obtained for a rectangular plate which is subjected to thermal loads. In functionally graded materials (FGMs) the material properties (such as modulus of elasticity, coefficient of thermal conductivity and coefficient of thermal expansion) are functions of coordinates, specially the thickness. Therefore, the stability equations are coupled in terms of in-plane and out-plane displacement components. Introducing a new analytical method and doing some mathematical calculations, three stability equations are converted to three independent equations. It is assumed that the plate is simply supported along the edges parallel to y axis, so the Levy solution is considered as the solution method. Imposing different boundary conditions on the solution of the stability equations, a system of homogenous algebraic equations is obtained. To have non-trivial solutions, the determinant of coefficients is equal to zero which results in determining the buckling temperatures. The smallest buckling temperature is known as the critical buckling temperature. Finally, the critical buckling temperaturesfor plates with different boundary conditions, some index of FGM and various aspect ratios and thickness to side ratios are presented in tables and figures.

Keywords:

Thermal buckling , Classical plate theory , Functionally graded , Levy solution , Rectangular plate