Hygrothermal Buckling and Vibration Analysis of BD-FGM Sandwich Plates via a Meshfree Moving Kriging Approach

This study presents a computational method for investigating the hygrothermal buckling and vibration behavior of porous bi-directionally functionally graded material (BD-FGM) sandwich plates. A quasi-3D higher-order shear deformation theory is adopted to capture detailed deformation mechanics under combined hygrothermal conditions, while both uniform and graded porosity distributions are incorporated to reflect realistic microstructural effects. The formulation is implemented using a moving Kriging meshfree scheme, which removes mesh dependency and satisfies boundary conditions exactly through its Kronecker delta property. Numerical investigations explore the influence of porosity coefficients, temperature gradients, material gradation, geometric ratios, and boundary constraints on stability and vibration responses. The results show that porosity distribution and gradient index strongly affect thermal stability boundaries and modal characteristics, with clamped plates exhibiting higher stiffness-induced shifts in natural frequencies compared to simply supported ones. Geometric factors such as aspect and thickness ratios further modulate sensitivity to hygrothermal environments. The proposed approach provides accurate and convergent predictions across a wide range of boundary conditions and parameter variations, offering a reliable basis for the design and analysis of porous BD-FGM sandwich plates in demanding thermal operating environments.