Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply

Numerical solutions obtained by the meshless local Petrov–Galerkin (MLPG) method are presented for transient thermoelastic deformations of functionally graded (FG) beams. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. In this study, the MLPG weak formulations associated with the governing equations of the transient-state thermal equilibrium and quasi-static mechanical equilibrium are given. The penalty method is adopted to efficiently enforce the essential boundary conditions, and the test function is chosen to equal the weight function of the moving least squares approximation. An example is demonstrated for an FG beam with thermoelastic moduli varying exponentially through the thickness direction under a nonuniformly convective heat supply. Results obtained from the MLPG method are found to agree well with those by the analytical solution. The nonhomogeneity of the material properties on the thermo-mechanical response of the FG beam is investigated. It is shown that temperature and deformation fields of FG beams in a transient state differ substantially from those at the steady state. Besides that, the rate of change of the heat supply on the transient responses is also delineated.