Post-buckling of functionally graded microplates under mechanical and thermal loads using isogeomertic analysis

Abstract

The present study uses the isogeometric analysis (IGA) to investigate the post-buckling behavior of functionally graded (FG) microplates subjected to mechanical and thermal loads. The modified a strain gradient theory with three length scale parameters is used to capture the size effect. The Reddy third-order shear deformation plate theory with the von Kámán nonlinearity (i.e., small strains and moderate rotations) is employed to describe the kinematics of the microplates. Material variations in the thickness direction of the plate are described using a rule of mixtures. In addition, material properties are assumed to be either temperature-dependent or temperature-independent. The governing equations are derived using the principle of virtual work, which are then discretized using the IGA approach, whereby a C 2-continuity requirement is fulfilled naturally and efficiently. To trace the post-buckling paths, Newton's iterative technique is utilized. Various parametric studies are conducted to examine the influences of material variations, size effects, thickness ratios, and boundary conditions on the post-buckling behavior of microplates.

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

“…assumed. The buckling for the plate with nonsymmetric pore distribution under SSSS and SCSC boundary conditions is not possible, because by applying the small axial load, these plates undergo lateral deformation [92][93][94][95].…”

Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory

“…in which K T is the tangent stiffness matrix given in details in [56]. After the increment displacement vector δd (i) is computed, the displacement vector at the (i + 1) th iteration is computed by…”

“…Therefore, the geometrical nonlinearity should be considered in the analyses of microplates. However, no literature has been reported for the nonlinear analysis of FG micropaltes based on the MST except a recent study on post-buckling of microplates conducted by Thai et al [56]. Therefore, the aim of this paper is to propose an effective numerical approach to predict the geometrically nonlinear responses of FG microplates based on the MST and the IGA approach.…”

A Size-Dependent Finite Element Method for the 3D Free Vibration Analysis of Functionally Graded Graphene Platelets-Reinforced Composite Cylindrical Microshells Based on the Consistent Couple Stress Theory

“…Incorporating the displacement model of the higher-order shear deformation theory into the MCST, Lyu et al [ 33 ] investigated the thermo-electro-mechanical free vibration and buckling behaviors of an FG piezoelectric porous cylindrical microshell. Based on the modified strain gradient theory, Thai et al [ 34 ] presented an isogeometric analysis (IGA) for studying the postbuckling behavior of an FG microplate subjected to mechanical and thermal loads. In their formulation, the kinematic model of Reddy’s refined shear deformation theory (RSDT) and the von Kármán geometrical nonlinearity (VKGN) were employed to describe the deformation of the microplate.…”