Static analysis of size-dependent FGM micro plate and shell panels under thermo-mechanical loading using exact shear correction factor

This study investigates the bending and stress behavior of functionally graded material (FGM) microplates and shell panels under thermomechanical loading, using the rule of mixtures (ROM) and local representative volume elements (LRVE). The formulation integrates first-order shear deformation theory (FSDT) with the modified couple-stress theory (MCST) to establish a size-dependent framework, and the governing equations are rigorously derived from Hamilton's principle. A neutral surface approach, along with an exact shear correction factor, is used to improve analysis accuracy. A finite element model is developed using an eight-noded isoparametric element with five degrees of freedom per node. The model represents an FGM panel with a pure ceramic upper layer and a pure metal lower layer, where temperature-dependent material properties are graded through the thickness. The effective properties are calculated using the ROM and LRVE. Aluminum oxide (Al2O3) and titanium alloy (Ti-6Al-4V) are selected as the ceramic and metallic constituents, respectively. The accuracy of the proposed formulation is first established by validating it against existing results. Subsequently, a comprehensive parametric analysis explores the effects of key parameters, including the material length-scale ratio, shear correction factor, panel geometry, and boundary conditions, on the structural performance. The findings of this study reveal that size-dependent effects significantly influence the bending behavior and stress distribution of FGM microplates and shell panels under thermomechanical loading. It is also observed that with the use of the exact shear correction factor, the results for bending and stress for FGM microplates and shell panels under thermo-mechanical loading obtained using ROM and LRVE are more accurate than those obtained using the conventional shear correction factor. Notably, the study is useful for microstructural applications involving the thermomechanical analysis of advanced micro-scale engineering structures, such as MEMS devices, sensors, actuators, and resonators, operating under coupled mechanical and thermal conditions.