Numerical investigation of the free-edge effect in cross-ply shells

Abstract

The effect of stress concentrations on the boundary of layers at the free surface of cross-ply composites (which in the literature received the name "edge effect" [1, 2]), being one of the most serious causes of failure of structures, was repeatedly analyzed by numerical methods (a detailed review of the relevant publications was provided in [3]) as well as on the basis of simplified approaches [1, 2]. in both cases the problem of generalized plane strain of an infinitely long strip was involved. The present work investigates an analogous effect in cross-ply shells of revolution on the basis of the finite-element solution of the axisymmetric problem of the theory of elasticity. In selecting the approach, we took into account that the finite element method (FEM) makes it possible to describe most reliably the effects at the free edge of a strip, and this received experimental confirmation [4]. We deal with a shell of revolution referred to as the triorthogonal coordinates cq, c~2, a 3 of which the first two are the lines of the principal curvatures of the inner surface (a 1 is the meridian), and the %-axis h'~s the direction of the outer normal to a 1, a 2. The shell was obtained by the crosswise placing of unidirectionally reinforced layers at the angles (--1)n+17 (the angle of reinforcement 7 is formed by the direction of reinforcement and the tangent to the meridian, n is the number of the layer counted from the inner surface). Each layer in the axes correlated with the direction of reinforcement is regarded as transversely isotropic, and its mechanical characteristics are determined by the well-known averaging formulas [5]. In the coordinates al, a 2, a 3 such a layer is cylindrically anisotropic with one plane of elastic symmetry, viz., the tangent to the surface, which is equidistant to the coordinate plane, and the rigidity matrix C of Hooke's generalized law