A finite element based global–local theory for static analysis of rectangular sandwich and laminated composite plates

In the present paper, a global–local theory with three-dimensional elasticity correction is developed for stress and deformation analysis of the multilayered and sandwich plates. The governing equations are derived based on the principle of minimum potential energy. The coupled governing equations are solved based on a finite element procedure uses the second-order Lagrangian elements and a Galerkin-type formulation. Results of this theory are accurate for both thin and thick plates. The transverse shear stresses are extracted based on the three-dimensional theory of elasticity. Thus, the continuity of the interlaminar transverse shear stresses is satisfied a priori. The proposed finite element formulation is implemented using MATLAB software. Results revealed that, while the accuracy of the present theory is comparable to that of the three-dimensional theory of elasticity and sometimes (e.g., when a very soft core is used) is higher than the high-order zigzag theories, the presented solution approach is computationally more economic. Finally, a comprehensive parametric study including evaluating the influences of the lamination scheme, number of layers, plate aspect ratio, side-to-thickness ratio, and material properties variations on the in-plane stresses, transverse shear stresses, and displacement components is performed.