Higher-order shear-deformable two dimensional hierarchical beam elements for laminated composites

Abstract

This paper presents a new two dimensional curved beam element formulation with higher-order transverse shear deformation for linear static analysis of laminated composites. The derived displacement approximation in the transverse direction can be of an arbitrary desired polynomial order p thereby permitting strains of at least order (p - 1). The element formulation provides displacement continuity across the interelement boundaries. The element properties are derived using the principle of virtual work and the hierarchical element approximation. The formulation is presented for generally orthotropic and laminated composite materials. Numerical examples are presented to demonstrate the accuracy, simplicity of modelling, effectiveness, faster rate of convergence and overall superiority of the present formulation.