Finite element formulation for thin-walled open composite beams including the effect of flexural and torsional shear deformation

In this paper we derive the field of displacements and strains for thin-walled open composite beams with composite laminated material including in their kinematics flexural and torsional shear deformations effects. The equilibrium equations are defined through the variational formulation and show that is possible to formulate C-o finite elements taking into account the torsional shear deformation. Stressstrain relationships for the cross-section of thin-walled composite beams are obtained by extending first-order laminate (FSDT: first-order shear deformation) theory and using a "free stress resultant condition at the boundary". Three different one-dimensional finite elements with C-o continuity are formulated for the study of thin-walled open composite beams and they are labelled as BSW (beam with shear and warping). The influence of the integration strategy in the BSW elements is evaluated via the shear-locking phenomenon and the rate of convergence for displacements and rotations. The stiffness matrix integration is compared using exact and reduced integration methods. Examples of pure torsion and flexo-torsion in a cantilever composite beam are performed. Numerical results are compared to those reported by other authors. (C) 2013 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L.U. All rights reserved.