An improved high-order Kriging mesh-free approach for nonlinear thermal buckling of porous FG beams

This study investigates the nonlinear thermal buckling behavior of porous functionally graded (FG) beams using a novel mesh-free approach. The approach combines the Kriging method with an asymptotic numerical method to model the thermal response of FG beams composed of a ceramic–metal mixture with a varying volume fraction and uniform porosity. The governing equations are derived from Timoshenko beam theory, and a consistent linearization method is used to decouple the nonlinear system. The decoupled system is solved numerically using a high-order Kriging mesh-free method, enhanced by Kriging shape functions and a Taylor series-based continuation procedure. The Kriging method offers high accuracy in interpolation and the ability to handle complex geometries and material distributions. The proposed method is validated through a comparative study on transverse FG beams, showing good agreement with results from the finite element method (FEM) and existing literature. Key parameters such as porosity and material distribution are evaluated for their effect on the thermal buckling behavior of FG beams under various loading conditions. This work offers significant advancements in the analysis of porous FG beams, providing a more accurate and efficient computational tool for complex structural problems.