Some studies on finite elements for laminated composite plates

Abstract

This paper is concerned with the analysis of plates made of continuous fibre reinforced laminated composite materials, using the Finite Element Method. Specifically the study concerns the behaviour of laminated plates including transverse shear deformations, and transverse normal stresses and strains. Three displacement based finite elements based on three different higher-order theories have been developed. The three different displacement functions have been expanded as straight-forward power series in terms of thickness coordinate and mid-plane variables, resulting in three, five and six degrees of freedom per node. The highest order displacement model under consideration assumes a cubic in-plane strain field, parabolic transverse shear strain field, and a linear transverse normal strain field. Based on the assumed displacements, nine-node Lagrangian isoparametric element stiffness matrices and the corresponding load vectors have been derived. The objective of this study is to evaluate the performance of above derived finite elements. The convergence characteristics and accuracy of these finite elements have been established by applying them to specific problems, and comparing the results with each other, and with the three-dimensional elasticity solutions, other closed-form solutions, and other finite element method based solutions for the same problems, when such results are available. In this paper the finite elements developed above have also been used to study the effects of plate width-to-thickness ratio, material anisotropy, number of layers, and the errors in the layer orientations on the response of rectangular and square symmetrically laminated composite plates subjected to uniformly distributed normal loads and sinusoidally distributed normal loads.