Semi-Analytical State-Space Differential Quadrature for Thermal Buckling of FG Plates under 3D Nonuniform Heating

Abstract

This study investigates the thermal buckling behavior of Functionally Graded Material (FGM) plates subjected to a general three-dimensional (3D) non-uniform temperature field, which varies both in the plane and through the thickness. Such a complex thermal load scenario is critical for realistic design but poses significant analytical challenges. To address this, an advanced semi-analytical solution framework is developed by synthetically combining the state-space method (SSM) and the differential quadrature method (DQM). The SSM elegantly handles the continuous variation of material properties and temperature along the thickness direction, reducing the 3D problem to a state-space formulation. The DQM then efficiently discretizes the in-plane differential operators and boundary conditions. This coupled SSM-DQM approach accurately transforms the thermo-elastic buckling problem into a standard eigenvalue problem. The proposed method is first validated against existing solutions for degenerate cases. A comprehensive parametric study then reveals the profound influence of the 3D temperature gradient profile, material gradient index, and plate aspect ratio on the critical buckling temperature. Results demonstrate that simplified temperature assumptions can lead to substantial errors, underscoring the necessity of employing a full 3D thermal load model for the safe design of advanced FGM structures in extreme thermal environments.