A refined asymptotic theory and computational model for multilayered composite plates Original Research Article

The asymptotic theory of multilayered composite plates developed recently is refined to embrace the shear deformation theory. The derivation is based on application of asymptotic expansion to the Hellinger-Reissner variational functional in which the displacements and transverse stresses are taken to be the functions subject to variation. By introducing rotations as auxiliary variables in the asymptotic formulation, the shear deformation theory of laminated plates arises naturally as the first-order approximation to the three-dimensional theory. Higher-order corrections are determined in an adaptive and hierarchic way. The computational model is constructed on the basis of the asymptotic expressions of the H-R functional in conjunction with the finite element method, in which the displacements and transverse stresses may be interpolated independently. Through successive ntegration, the transverse stress degrees-of-freedom are condensed at the element level, resulting in rotations and midplane displacements as basic unknowns in the system equations. In the model the lateral boundary conditions are satisfied exactly. The edge conditions associated with each level are shown to be similar to the ones in the 2D theory of Mindlinʹs plates, which can be easily implemented in the computation. The performance of the model is illustrated by example problems.