Two-Dimensional Finite Element Method for Modeling Edge Effects in Cross-Ply Laminates

Abstract

A 2-dimensional finite element (FE) method, based on an approximate analytical solution, is developed to define accurately stress fields and boundary layer width in symmetrically laminated composites. A better insight into the edge effect and delamination failure of cross-ply laminates is attained through a physical explanation of the mathematical FE solution. While some other solutions failed, the present FE solution obtains accurate results using a limited number of elements, and therefore reduces computer storage and computation time. A perturbation technique is employed to derive shape functions for the free edge boundary region, which properly describes the physics of sudden exponential growth of stress field in the vicinity of the edge. An original and comprehensive FE computer program is developed, using these specific shape functions, special numerical integration, and mesh generation algorithms. Results for bidirectional laminates under uniaxial extension are presented and compared with finite difference, FE, and approximate analytical solution.
 HIGHLIGHTS
 
 Defining accurately stress field in free edge region is the main challenge
 Shape functions based on perturbation solution yield accurate results
 Boundary layer width is proportional to geometric ratio of laminates
 Finer mesh in boundary region is required for small geometric ratio laminates
 A huge number of finite elements are needed to determine narrow boundary width
 
 GRAPHICAL ABSTRACT