In this work, Lekhnitskij’s stress functions are introduced in each anisotropic layer of composite laminate. This ensures that the approximate solutions of the present approach satisfy exactly the equilibrium equations in all parts of the laminate including the interfacial corner regions with steep stress gradients. Furthermore, the traction-free boundary conditions and the continuity of interlaminar stresses are exactly satisfied, while the compatibility of strains and the interfacial continuity of displacements are enforced in an averaged sense through the condition of stationarity of complementary energy.
Besides the constitutive assumption of linear anisotropic elasticity for individual layers, the only assumption introduced in the present paper is that the stress functions in each layer are polynomial functions of the thickness coordinate. No a priori assumption is made concerning the dependence of the stress functions on the coordinate parallel to the interface. The form of this dependence is obtained by the applications of the principle of complementary energy.
The variational equations contain three load parameters characterizing the axial extension and bending and twisting of the strip, and can be written as a system of linear ordinary differential equations with constant coefficients. This system of equations together with homogeneous boundary conditions along the free edges define an eigenvalue problem. Analytical expressions and the needed matrix elements are obtained in terms of the layer elasticity, thicknesses, and orientation angles by using the symbolic program MACSYMA. FORTAN codes are developed for solving the eigenvalue problem and evaluating the interlaminar stresses along the interfaces under various strain loads.