J. Argyris et L. Tenek, BUCKLING OF MULTILAYERED COMPOSITE PLATES BY NATURAL SHEAR DEFORMATION MATRIX-THEORY, Computer methods in applied mechanics and engineering, 111(1-2), 1994, pp. 37-59
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 de
composition and lumping concept, evolved through the adoption of a nat
ural 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 fa
ctors can directly adjust the element's transverse shear stiffness for
thicker plates while retaining a direct linear strain distribution ac
ross the element thickness. Subsequently, the geometric stiffness, whi
ch arises mostly from the rigid body movements of the element is deriv
ed, and the corresponding buckling eigenvalue problem is stated. The c
omplete 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 comp
letely 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 thi
ck plates from a higher-order shear deformation theory, as well as fro
m theory of elasticity.