Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the element-free Galerkin method

•Thermal buckling of skew and trapezoidal functionally graded plates is studied.•The element-free Galerkin method is employed to study the thermal buckling.•The effect of skew angle on the critical temperature differences is examined.•The critical temperature difference is increased by increasing the aspect ratio.•The critical temperature difference is decreased by increasing the thickness ratio.

In this paper, thermal buckling of functionally graded skew and trapezoidal plates is investigated using the element-free Galerkin method. The shape functions are constructed using the moving least squares (MLS) approximation and the essential boundary conditions are introduced into the formulation through the use of the Lagrange multiplier method and the orthogonal transformation techniques. The material properties are assumed to vary as a power form of the thickness coordinate. Uniform, Linear and nonlinear temperature rise across the thickness are considered. The effects of aspect ratio, thickness ratios, gradient index and skew angle on the critical buckling temperature difference are examined.