Boundary Point Least Squares Analysis of the Free Edge Effects in Some Unidirectional Fiber Composites

Abstract

The effect of a free edge on the stress distribution in several uni directional composite plates is presented. Plates with one, two, and three rows of equally spaced fibers are considered. The fibers and matrix are elastic and isotropic. Two types of loading conditions are investigated. The first is a uniform extension transverse to the fiber direction. The second is a linearly varying "bending" displacement transverse to the fiber direction. Stress and displacement solutions are obtained by the boundary point least squares method. For both loading conditions considered, the results show that the effect of the free edge extends only to the outer fiber nearest the free edge and the stress distribution in and around the remaining "inside" fibers is essentially equivalent to stresses for a fiber embedded in a doubly periodic array. For the case of uniform extension, effective transverse moduli are computed for the one, two, and three fiber plates and compared with the effective transverse modulus for an infinite plate.