A shear-deformable, doubly-curved finite element for the analysis of laminated composite structures

A doubly-curved, shear-deformable finite element is developed for the analysis of laminated composite structures. The Kirchhoff hypothesis is relaxed to allow for shear deformations; as a result, three independently prescribed rotations as well as three displacements are specified at each of the eight nodes of the element. The constitutive equations are utilized to calculate the in-plane stresses for each layer of the laminated structure. In order to establish an appropriate variation through the thickness, the transverse shear stresses are found by integrating the equilibrium equations for each layer. An integration procedure using a finite difference approach is performed to evaluate the transverse shear stresses. Excellent results have been achieved for a three-layered, helically-wound cylinder with simply-supported and clamped ends.