A beam finite element based on layerwise trigonometric shear deformation theory

Abstract

A simple one-dimensional beam finite element, based on layerwise trigonometric shear deformation theory, is presented. The element has two nodes and only three degrees of freedom per node. Yet, it incorporates through the thickness sinusoidal variation of in-plane displacement such that shear-stress free boundary conditions on the top and bottom surfaces of the beam element are satisfied and the shear-stress distribution is realistic in nature. Constitutive relations between shear-stresses and shear-strains are satisfied in all the layers, and, therefore, shear correction factor is not required. Compatibility at the layer interface in respect of in-plane displacement is also satisfied. It is to be noted that the element developed is free from shear locking. The results obtained are accurate and show good convergence. Unlike many other elements, transverse shear-stresses are evaluated directly using constitutive relations. The efficacy of the present element is demonstrated through the examples of static flexure and free vibration.