Linear thermal bending analysis of functionally graded square plate under different boundary conditions and geometric effects

A C 0 FE framework is developed in this study through the application of a penalty method on a C 1 five-variable “higher-order shear deformation theory”. The method is tailored for analysing the linear-thermal-bending response of “functionally graded material” (FGM) plates. The properties of FGMs are estimated employing rule of mixtures, while the governing relations are obtained by implementing virtual work approach. For discretisation, a 9-noded Lagrange element incorporating 7 degrees of freedom are employed to each node. To assess performance, numerical studies are conducted by comparing results with Reddy’s TSDT theory and a “non-polynomial higher-order shear deformation theory” (NPHSDT). finite element method (FEM) method is applied for analysing thermal flexural response of “FGM-plates” under diverse environments. The proposed formulation’s reliability is established through validation against reference solutions reported in prior studies. Furthermore, a detailed parametric study explores the influence of material gradation, span-tothickness ratio, thermal expansion coefficient ratio, and boundary constraints. Overall, the research provides meaningful insights into thermal bending characteristics of “FGM-plates”, supporting the efficient design and structural evaluation of advanced engineering systems.