Thermo-mechanical buckling behavior of FG GNP reinforced micro plate based on MSGT

Thermal and mechanical buckling analysis of micro plate reinforced with functionally graded (FG) graphene nanoplatelets (GNPs) is studied in this paper based on modified strain gradient theory (MSGT). For description of kinematic relations, two higher order shear deformation theories including third order shear deformation theory and sinusoidal shear deformation theory are employed simultaneously. Size-dependency is accounted in governing equations of thermal buckling by application of modified strain gradient formulation including three micro length scale parameters. Distribution of graphene nanoplatelets along the thickness direction is assumed based on various known models including Parabolic, linear and uniform. Halpin-Tsai model and rule of mixture are used for calculation of the effective modulus of elasticity and Poisson's ratio, respectively. The outputs of this work are verified through comparison with existing numerical results based on various theories and methods. Thermal buckling loads are calculated based on analytical method in terms of significant parameters such as weight fraction of GNPs, various distribution of GNPs, three micro length scale parameters, some non-dimensional geometric parameters such as side length to thickness ratio and thickness to micro length scale ratio.