DERIVATION OF PLATE-THEORY ACCOUNTING ASYMPTOTICALLY CORRECT SHEAR DEFORMATION

The focus of this paper is the development of linear, asymptotically c orrect theories for inhomogeneous orthotropic plates, for example, lam inated plates with orthotropic laminae. It is noted that the method us ed can be easily extended to develop nonlinear theories for plates wit h generally anisotropic inhomogeneity. The development, based on varia tional-asymptotic method, begins with three-dimensional elasticity and mathematically splits the analysis into two separate problems: a one- dimensional through-the-thickness analysis and a two-dimensional ''pla te'' analysis. The through-the-thickness analysis provides elastic con stants for use in the plate theory and approximate closed-form recover ing relations for all truly three-dimensional displacements, stresses, and strains expressed in terms of plate variables. In general, the sp ecific type of plate theory that results from variational-asymptotic m ethod is determined by the method itself. However, the procedure does not determine the plate theory uniquely, and one may use the freedom a ppeared to simplify the plate theory as much as possible. The simplest and the most suitable for engineering purposes plate theory would be a ''Reissner-like'' plate theory, also called first-order shear deform ation theory. However, it is shown that construction of an asymptotica lly correct Reissner-like theory for laminated plates is not possible in general. A new point of view on the variational-asymptotic method i s presented leading to an optimization procedure that permits a derive d theory to be as close to asymptotical correctness as possible while it is a Reissner-like. This uniquely determines the plate theory. Nume rical results from such an optimum Reissner like theory are presented. These results include comparisons of plate displacement as well as of three-dimensional field variables and are the best of all extant Reis sner-like theories. Indeed, they even surpass results from theories th at carry many more generalized displacement variables. Although the de rivation presented herein is inspired by, and completely equivalent to , the well-known variational-asymptotic method, the new procedure look s different. In fact, one does not have to be familiar with the variat ional-asymptotic method in order to follow the present derivation.