Isogeometric analysis of thermal buckling in FGM plates considering crack contact constraints

Abstract

This study presents a comprehensive thermal buckling analysis framework for functionally graded material (FGM) plates with embedded cracks subjected to uniform thermal loading. A novel numerical methodology has been developed to systematically investigate the mechanistic influence of crack characteristics on structural stability. The theoretical formulation integrates the first-order shear deformation theory (FSDT) with von Kármán geometric nonlinearity, incorporating the Heaviside function to accurately model displacement discontinuities across crack surfaces. The computational framework employs isogeometric analysis (IGA) for precise geometric representation of crack configurations and utilizes the augmented Lagrangian method to solve the nonlinear equilibrium equations with crack contact constraints. The numerical results reveal three key findings: (1) The critical buckling factor ratio exhibits a positive correlation with crack length, demonstrating a progressive increase with crack extension; (2) Crack location and orientation induce localized discontinuities in the buckling mode patterns, significantly altering the deformation characteristics; (3) Plate geometry parameters, specifically the aspect ratio and thickness, substantially influence the critical buckling factor ratio, while the material gradient index shows negligible effects. Through systematic parametric studies, this research establishes quantitative relationships between crack parameters and thermal buckling behavior. These findings provide fundamental insights for the thermo-mechanical design of FGM structures with inherent defects, particularly in high-temperature applications where structural integrity is paramount.