Application of coupled polynomial displacement fields to laminated beam elements

A 2-noded curved composite beam element with three degrees of freedom per n ode is proposed for the analysis of laminated beam structures. The formulat ion 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 assum ed for the transverse displacement w. The field interpolations for the long itudinal displacement u and section rotation theta are derived using the el emental equilibrium equations. The procedure leads to field interpolations that are coupled by means of coefficients, which are functions of geometric al and material properties of the element. The efficacy of these coupled po lynomial fields in improving the accuracy and convergence characteristics o f the proposed element has been demonstrated by a series of numerical examp les. The lay-up sequence does not affect the accuracy of the element, unlik e the conventional 2-noded elements, which make use of independent field in terpolations. The element does not exhibit membrane and shear locking. The test problems prove the versatility of the element for the analysis of curv ed and straight laminated beams. (C) 2000 Elsevier Science Ltd. All rights reserved.