Asymptotic Construction of Reissner-Like Models for Composite Plates With Accurate Strain Recovery

The focus of this paper is to develop an asymptotically correct theory for composite laminated plates when each lamina exhibits monoclinic material symmetry. The development starts with formulation of the three-dimensional, anisotropic elasticity problem in which the deformation of the reference surface is expressed in terms of intrinsic two-dimensional variables. The Variational Asymptotic Method is then used to rigorously split this three-dimensional problem into a linear one-dimensional normal-line analysis and a nonlinear two-dimensional “plate” analysis accounting for transverse shear deformation. The normal-line analysis provides a constitutive law between the generalized, two-dimensional strains and stress resultants as well as recovering relations to approximately express the three-dimensional displacement, strain and stress fields in terms of plate variables calculated in the “plate” analysis. It is known that more than one theory that is correct to a given asymptotic order may exist. This nonuniqueness is used to cast a strain energy functional that is asymptotically correct through the second order into a simple “Reissner-like” plate theory. Although it is true that it is not possible to construct an asymptotically correct Reissner-like composite plate theory in general, an optimization procedure is used to drive the present theory as close to being asymptotically correct as possible while maintaining the beauty of Reissner-like formulation. Numerical results are presented to compare with the exact solution as well as a previous similar yet very different theory. The present theory has excellent agreement with the previous theory and exact results.