Three-dimensional stress analyses around cutouts in laminated composites by special hybrid finite elements

Abstract

The distribution of stresses around some cutouts in laminated composites is analyzed by using the combination of two kinds of special hybrid stress multilayer finite elements. One kind of the three-dimensional special finite element contains a traction-free cylindrical surface and the other contains a traction-free planar surface. Both of these special finite elements are derived based on a modified complementary energy principle. The expressions of six stress components in each kind of element are derived, such that the homogeneous equilibrium equations in each layer, the continuity of the transverse stresses on the interlayer surface, and the traction-free boundary conditions over the designated surfaces are satisfied a prior, while the interelement reciprocity traction is satisfied a posterior in a variational sense. All components of displacement are included since bending–stretching coupling may occur. Examples have indicated that the combination of these special multilayer finite elements is far superior in predicting the distribution of circumferential stresses and transverse stresses for laminates with holes and notches when only a very coarse element mesh is used near the free edge of the cutouts.