Analysis of laminated beams with a layer-wise constant shear theory

Based on generalized laminate plate theory, the formulation of a one-dimensional beam finite element with layer-wise constant shear (BLCS) is presented. The linear layer-wise representation of in-plane displacements permit accurate computation of normal stresses and transverse shear stresses on each layer for laminated beams with dissimilar ply stiffnesses. The BLCS formulation is equivalent to a first-order shear deformation beam theory (Timoshenko beam theory) on each layer. For the accurate computation of interlaminar shear stresses, the layer-wise constant shear stresses obtained from constitutive relations are transformed into parabolic shear stress distributions in a postprocessing operation described in detail. The accuracy of the BLCS element is .demonstrated by solving several numerical exampl~s reported in the literature. While retaining the simplicity of a laminated beam theory, the element predicts results as accurate as much more complex elasticity analyses, and it is suitable to model frame-type structures.