Nonlinear Thermo-Mechanical Response of Bi-Directional Functionally Graded Porous Beams with Initial Geometrical Imperfection

In this paper, the nonlinear vibration and buckling of bi-directional functionally graded (2D-FG) beam subjected to thermal loading are examined via the higher-order shear deformable beam theory incorporating the von Kármán geometric nonlinearity. Two types of initial defects including the internal porosity distribution and external geometrical imperfection shape are taken into consideration. The temperature-dependent material property varying along the length and thickness following the power-law function is employed, and the porosities inside the 2D-FG beam with even and uneven distributions are considered. The initial geometrical imperfection is described by the product of trigonometric and hyperbolic functions, which can capture both global and localized imperfection shapes. The discrete equations of motion for the 2D-FG beam are established by using the differential quadrature method (DQM), and the derived function is solved by an iterative procedure. The nonlinear thermo-mechanical vibration and buckling of 2D-FG beams under uniform, linear, and nonlinear temperature loads are systemically compared. Moreover, several key factors such as 2D-FG indexes, porosity distribution, geometrical imperfections, as well as boundary conditions are investigated in detail. The proposed model and obtained results can be used to guide the optimization design of multi-functional and multi-graded materials serviced under thermal environment.