Finite Element Analysis of Laminated Composite Beams for Zigzag Theory using MATLAB

An efficient one dimensional finite element model has been presented for the static analysis of composite laminated beams, using the efficient layerwise zigzag theory. To meet the convergence requirements for the weak integral formulation, cubic Hermite interpolation is used for the transverse displacement and linear interpolation is used for the axial displacement and shear rotation. Each node of an element has four degrees of freedom. The expressions of variationally consistent stiffness matrix and the load vector are derived in closed form using exact integration. The formulation is validated by comparing the results with the computed 2D-FE results for composite symmetric and sandwich beams with various end conditions. The finite element model is free of shear locking. The present zigzag finite element results for natural frequencies, mode shapes of cantilever and clamped– clamped beams are compared with the two-dimensional finite element results obtained using ABAQUS to establish the accuracy of the zigzag theory FEM for dynamic response under these boundary conditions.