BUCKLING OF MULTILAYERED COMPOSITE PLATES BY NATURAL SHEAR DEFORMATION MATRIX-THEORY

The present study discusses buckling of multilayered composite plates from the standpoint of a natural shear deformation theory (NSDT) which is developed and shaped by means of matrix language on a model facet three-node triangular finite element. Isotropic, sandwich, and hybrid plates can also be treated. It is shown that by invoking a physical decomposition and lumping concept, evolved through the adoption of a natural coordinate system in harmony with the given element geometry, an assembly of three edge-beams is created and is solely responsible for the carrying of the transverse shear forces. Thus, three correction factors can directly adjust the element's transverse shear stiffness for thicker plates while retaining a direct linear strain distribution across the element thickness. Subsequently, the geometric stiffness, which arises mostly from the rigid body movements of the element is derived, and the corresponding buckling eigenvalue problem is stated. The complete derivation of the geometrical stiffness matrix is in principle reduced to a simple transformation of the nodal freedoms. The matrix formulation, as well as convergence of the triangular element are completely natural, and numerical experiments for simply supported plates reveal that the obtained buckling loads conform very well at the thin limit with results from classical plate theory, and for moderately thick plates from a higher-order shear deformation theory, as well as from theory of elasticity.