Highly accurate nonlinear three-dimensional finite element elasticity approach for biaxial buckling of rectangular anisotropic FGM plates with general orthotropy directions

Buckling of the orthotropic FGM plates has not been investigated so far. In the present paper, a highly accurate nonlinear three-dimensional energy-based finite element elasticity formulation is developed for buckling investigation of anisotropic functionally graded plates with arbitrary orthotropy directions. The material properties are assumed to have in-plane orthotropy and transverse heterogeneity. The formulation and results cover uniaxial compression and compression and tension-compression biaxial loading conditions. The governing equations are developed based on the principle of minimum total potential energy and solved based on finite element orthogonal integral equations. To achieve most accurate results, a full compatible Hermitian element with 168 degrees of freedom, which satisfies continuity of the strain and stress components at the mutual edges and nodes of the element a priori, is employed. A variety of loading combinations, orthotropy directions, and aspect ratios is considered and discussed in the results section to draw practical conclusions. Results reveal that when the external loads are exerted in the principal directions of the materials, higher strengths may be achieved.