Three-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 layer has to be treated as a distinct 3-D anisotropic body with the continuity of displacements and transverse stresses imposed between the layers. If adopting such a formulation, a finite element discretization of the multilayered structure would require, besides a large number of the in-plane elements. at least one element per layer in the through-thickness direction. Thus, a huge amount of degrees of freedom, proportional to the number of layers in the laminate, will be present in the 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 structures, the following approximate models are proposed and applied in the framework of the earlier developed 3-D Variational Deficient Approximation Function Approach: Globally Averaged Stiffness (GAS) model, where the actual step-wise variation of stiffnesses of the laminate are substituted 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 groups of adjacent layers in the laminate are represented as ''sub-laminates'' 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 variation is approximated by Bernstein polynomials using the method of least squares. Implementation of the above models and their accuracy is studied 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 thickness direction is used. (C) 1997 Elsevier Science Limited.