Application of coupled polynomial displacement fields to laminated beam elements

A 2-noded curved composite beam element with three degrees of freedom per node is proposed for the analysis of laminated beam structures. The formulation accounts for flexural, extensional and transverse shear loadings in the plane of the curved beam. The transverse shear flexibility based on first-order shear deformation theory is incorporated. A cubic polynomial is assumed for the transverse displacement w. The field interpolations for the longitudinal displacement u and section rotation θ are derived using the elemental equilibrium equations. The procedure leads to field interpolations that are coupled by means of coefficients, which are functions of geometrical and material properties of the element. The efficacy of these coupled polynomial fields in improving the accuracy and convergence characteristics of the proposed element has been demonstrated by a series of numerical examples. The lay-up sequence does not affect the accuracy of the element, unlike the conventional 2-noded elements, which make use of independent field interpolations. The element does not exhibit membrane and shear locking. The test problems prove the versatility of the element for the analysis of curved and straight laminated beams.