ON ASYMPTOTICALLY CORRECT LINEAR LAMINATED PLATE-THEORY

The focus of this paper is the development of asymptotically correct t heories for laminated plates, the material properties of which vary th rough the thickness and for which each lamina is orthotropic. This wor k is based on the variational-asymptotical method, a mathematical tech nique by which the three-dimensional analysis of plate deformation can be split into two separate analyses : a one-dimensional through-the-t hickness analysis and a two-dimensional ''plate'' analysis. The throug h-the-thickness analysis includes elastic constants for use in the pla te theory and approximate closed-form recovering relations for all thr ee-dimensional field variables expressed In terms of plate variables. In general, the specific type of plate theory that results from this p rocedure is determined by the procedure itself. However, in this paper only ''Reissner-like'' plate theories are considered, often called fi rst-order shear deformation theories. This paper makes three main cont ributions: first it is shown that construction of an asymptotically co rrect Reissner-like theory for laminated plates of the type considered is not possible in general. Second, a new point of view on the variat ional-asymptotical method is presented, leading to an optimization pro cedure that permits a derived theory to be as close to asymptotical co rrectness as possible. Third, numerical results from such an optimum R eissner-like theory are presented. These results include comparisons o f plate displacement as well as of three-dimensional field variables a nd are the best of all extant Reissner-like theories. Indeed, they eve n surpass results from theories that carry many more generalized displ acement variables. Copyright (C) 1996 Elsevier Science Ltd