3D B-spline finite element nonlinear elasticity buckling analysis of rectangular FGM plates under non-uniform edge loads, using a micromechanical model

Three-dimensional buckling analysis of the functionally graded plates has not been investigated under non-uniform in-plane compressive loads so far. The only available work in this field has been performed based on the first-order shear deformation theory, employing the simple rule of mixtures. In the present paper, a non-linear three-dimensional energy-based elasticity analysis is developed for buckling investigation of functionally graded plates subjected to non-uniform in-plane compressions. The comparative studies performed in the present paper reveal that the rule of mixtures is generally inappropriate for determination of the effective material properties. For this reason, a micromechanics-based model is used instead. In contrast to the common displacement-based numerical or semi-analytical elasticity analyses (with C0-continuity), present formulations are C2-continuous due to using the proposed 3D cubic B-spline element. Buckling analysis is accomplished through a two-step procedure wherein the prebuckling stresses are determined first. A non-linear weighted-residuals-based finite element solution is used. The buckling load associated with each of the adopted 8 types of the load distribution patterns is detected based on a generalized geometric stiffness concept. Various and comprehensive parametric studies are accomplished and various boundary conditions are considered to extract more precise conclusions.