Consistent 2D formulation of thermoelastic bending problems for FGM plates

In this paper, we present the development of completely 2D formulation for bending of functionally graded plates subjected to stationary thermal loading. Consistently with the assumptions made in plate bending theories, the temperature field in 3D domain is expanded into low order power-law series with respect to transversal coordinate and the original 3D formulation (governing equation and boundary conditions) is recast according to physical principles into 2D formulation. A unified formulation is developed using the assumptions of three plate bending theories such the Kirchhoff-Love theory for bending of thin plates (KLT) and the shear deformation plate theories of the 1st and 3rd order (FSDPT, TSDPT) valid for thick plates too. The derivation is performed with assuming the power-law gradation of material coefficients (such as the Young modulus, linear thermal expansion coefficient, and heat conduction coefficient) across the plate thickness. For variation of material coefficients and plate thickness within the mid-plane, arbitrary continuous function is allowed. In numerical simulations, the derived formulation is implemented numerically by using the strong formulation and mesh-free Moving Least Square-approximation. The original PDE with high order derivatives are decomposed into a system of 2nd order PDE.