The analytical tools and corresponding computational algorithms, while applicable to the analysis of stress fields in composite structural parts, have to satisfy certain basic principles. The main requirement is to satisfy all of the necessary internal continuity conditions on displacements and transverse stresses at interfaces. This can be used as the basis for evaluation of applicability of a variety of finite element models developed recently for 3-D analysis of stress fields in both thick and thin laminated anisotropic plates.

A 3-D analysis of laminated anisotropic plates can be provided effectively using the proposed sub-layerlspline approximation approach that incorporates : (1) formulation of a 3-D elasticity problem for a laminated structure in terms of a variational principle; (2) through-the-thickness division of each physical layer into an arbitrary number of “sub-layers” having purely computational meaning; (3) in-plane division of each layer into a number of 2-D elements; (4) through-the-thickness approximation of displacements with “deficient” spline functions having discontinuous first derivatives at all of the physical interfaces; (5) in-plane approximation of displacements with continuously differentiable spline functions; (6) derivation of a system of algebraic equations (or ordinary differential equations in the case of dynamic problems) using a variational equation; (7) solving the system with some numerical technique; (8) calculation of the displacements, strains, and stresses through the summation of the corresponding series using strain-displacement and stress-strain equations. Using this method, which is totally in the framework of the displacement-assumed approach, it is possible to satisfy with any desirable accuracy all the necessary internal and external boundary conditions imposed on displacements and/or stresses.

The high accuracy and efficiency of the method and the possibilities of the computer codes worked out on the basis of this method are demonstrated on the 3-D static bending problems for a laminated cross-ply plate: (i) simply supported sinusoidally loaded plate; (ii) simply supported uniformly loaded plate; (iii) cantilever sinusoidally loaded plate. The results for the problems (i) and (ii) are compared to the analytical and series solutions. Some specific features of stress concentrations near the clamped edge are revealed in the problem (iii).