A singular hybrid finite element analysis of boundary-layer stresses in composite laminates

Straight free-edge effects in laminated composites

“…Various ÿnite element methods such as conventional assumed displacement elements, isoparametric multilayer plate elements, hybrid stress multiplayer elements and special hybrid elements etc. have been suggested [1][2][3][4][5][6][7][8][9][10][11][12][13]. Bar-Yoseph [14] and Bar-Yoseph and Avrashi [15,16] also computed the stresses by the use of a new hybrid stress element based on a modiÿed Hellinger-Reissner principle with asymptotic expansion.…”

Finite Element Analysis of Free-Edge Delamination in Laminated Composite Specimens

“…Reissner's variational principle [8,9], (lobail-local model [10] etc., while the numerical solutions are based on finite difference [11,12] and finite element methods including displacement [13][14][15][16], stress [17] and hybrid [18,19] formulations. It was found that some of the solution techniques were only applicable under certain conditions.…”

“…One example is shovn in Figure (1) in vhich significant difference \ias obser\ed for or, stress distribution al,, the interface of [45/-45], laminate based on various solution techniques [19].…”

“…However, the credibility of various methods in predicting the or distribution shown in Figure (1 Most approximate solutions [2][3][4][5][6][7][10][11][12][13][14][15][16][17][18][19] are based uplon elasticity theory and treat the problem as a generalized plane strain case. This is because first of all, the classical and even many of the refined laminate theories, are single-layer theories which do not account for local effects such as geometric and material discontinuities, and the presence of a free-edge; secondly, use of discrete layered theory is very uneconomical and impractical from the computational stand point.…”

“…In order to have a pretise prediction of delamination behavior, an accurate estimate for the near-field stress distribution is essential. However, due to the singular nature of the boundary-layer stress field [19], an exact solution is currently unavailable, and discrepancies exist in the magnitude and even the sign of the computed interlaminar stresses near the free-edge ( Figure 1 [2] using a composite model essentially consisting of a set of anisotropic layers separated by isotropic adhesive layers. It was assumed that the isotropic layers, developed only interlaminar shear stresses, acting as an adhesive between the anisotropic layers.…”