Richard M. Barker

Three-dimensional finite-element analysis of laminated composites

Abstract A three-dimensional finite-element analysis treating the mechanical response of thick laminated composite plates in bending is presented. An isoparametric solid element with a cubic displacement expansion in planform and a linear variation through the thickness is used to model each layer of the laminate. The degrees-of-freedom of the element are retained at its boundaries so that interconnections between lamina with different fiber orientations can be made at their interfaces. An incore version of the conjugate gradient technique, which does not have bandwidth restrictions, is used to minimize the total potential energy of the system with the number of iterations to convergence being about one-fifth the total global degrees-of-freedom. Because a three-dimensional analysis is used, the effects of thickness-stretching, transverse shear, extension, and bending deformations are obtained. Comparisons with three-dimensional elasticity solutions are in excellent agreement and show the necessity of having individual elements for each layer when they have different fiber orientations and when the plates are thick.

Stress Concentrations Near a Discontinuity in Fibrous Composites

Stress concentration factors are defined for the fiber and matrix in an axially loaded unidirectional composite which has a discontinuous fiber Effects of variations in fiber volume fraction, end-gap size, and modulus ratio are studied by using a linearly elastic finite-element analysis Results show that the fiber stress concentration factors reach a maximum value of 1.5 and then remain relatively unchanged The matrix stress concentration factors, however, are shown to increase rapidly with decreasing end-gap size and increasing modulus ratio.

Effect of Modulus Ratio on Stress near a Discontinuous Fiber.

The effect of the fiber to matrix modulus of elasticity ratio varying from 1.0 to 200 was investigated for a two-dimensional plane-stress composite configuration having a simulated fiber volume fraction of 0.45 and containing a discontinuous fiber. Uniaxial loading parallel to the fibers was considered. Two independent techniques were used: moiré strain analysis and finite-element analysis. Displacements were measured from four experimental models by utilizing optical fringe-multiplication techniques. The finite-element method yielded stresses which agreed closely with those obtained from the experimental analysis. Matrix stress-concentration factor near the discontinuous fiber was found to increase rapidly with increasing modulus ratio, reaching a value of 20 for a modulus ratio of 200. The finite-element method was shown to be a valuable tool for micromechanical stress analysis of composite materials, and the accuracy of strain analysis by moiré-fringemultiplication techniques was demonstrated for problems containing sever strain gradients.

Finite Element Analysis of Bending-Extensional Coupling in Laminated Composites

pling. For example, the reduction of effective laminate stiffness due to coupling may depend on the modular ratio (E11~E22) and orientation of the individual lamina as well as on the type of loading and support conditions. To this end, the solutions to the equations of classical laminated plate theory presented by Whitney [1, 2, 3] for selected boundary value problems are of considerable value. Although the effects of coupling have not been completely described in these studies, several important conclusions have been made. It is the purpose of this paper to present numerical results of a finite element