Composite Beam Element with Layerwise Plane Sections

Abstract

Based on generalized laminate plate theory (GLPT), the formulation of a one-dimensional laminated beam finite element with layerwise constant shear (BLCS) is presented. BLCS formulation is equivalent to a first-order shear deformation beam theory (Timoshenko beam theory) on each layer, and a cross section of the beam therefore does not necessarily remain plane through the laminate, but only through each layer. Plane stress is assumed through both the thickness and width of the beam in the constitutive equation for a lamina. Details are presented for transforming the layerwise constant shear stresses obtained from constitutive relations into parabolic shear stress distributions. The layerwise representation of in-plane displacement through the thickness results in the formulation of a relatively simple beam element. Numerical analyses are presented for a three-node BLCS element integrated with two Gauss points. The accuracy of the element is evaluated by comparing the predictions to elasticity and experimental results.