3-DIMENSIONAL ANALYSIS OF THICK COMPOSITE PLATES WITH MULTIPLE LAYERS

A straightforward three-dimensional (3-D) analysis of thick laminated structures composed of many layers (in practical situations there may be dozens, even hundreds of them) is a computationally expensive task. Indeed, if a three-dimensional elasticity formulation is used, each l ayer has to be treated as a distinct 3-D anisotropic body with the con tinuity of displacements and transverse stresses imposed between the l ayers. If adopting such a formulation, a finite element discretization of the multilayered structure would require, besides a large number o f the in-plane elements. at least one element per layer in the through -thickness direction. Thus, a huge amount of degrees of freedom, propo rtional to the number of layers in the laminate, will be present in th e computational model. An analogous situation is faced when using any other numerical method. In order to develop accurate and, at the same time, computationally inexpensive 3-D analysis of multilayered structu res, the following approximate models are proposed and applied in the framework of the earlier developed 3-D Variational Deficient Approxima tion Function Approach: Globally Averaged Stiffness (GAS) model, where the actual step-wise variation of stiffnesses of the laminate are sub stituted by the ''effective'' stiffnesses of an ''equivalent'' single layer, calculated through the combined stiffness/compliance averaging procedure. Sub-Laminate Averaged Stiffness (SLAS) model, where the gro ups of adjacent layers in the laminate are represented as ''sub-lamina tes'' with their stiffnesses calculated through the combined stiffness /compliance averaging procedure analogous to GAS. Polynomial Stiffness Approximation (PSA) model, where the actual step-wise stiffness varia tion is approximated by Bernstein polynomials using the method of leas t squares. Implementation of the above models and their accuracy is st udied on the examples of cross-ply and angle-ply composite rectangular plates with symmetric and non-symmetric ply lay-ups. Accuracy of the results is evaluated by comparison with the Discrete Layer Stiffness ( DLS) model, where the actual step-wise stiffness Variation in the thic kness direction is used. (C) 1997 Elsevier Science Limited.