A new C0 continuous refined zigzag {1,2} finite element formulation for flexural and free vibration analyses of laminated composite beams

Abstract

This study presents a novel C0 continuous refined zigzag finite element formulation {1,2}, namely RZE{1,2}, for the bending and free vibration analyses of laminated composite beams. The Refined Zigzag Theory (RZT) effectively combines accuracy and computational efficiency, making it a robust approach for thin and thick laminated composite structures. The RZT eliminates the need for shear correction factors, thereby enhancing the overall streamline of the analysis process. The present RZE{1,2} formulation takes into account the transverse stretching by introducing quadratic through-thickness variations of deflection components. The governing equations of the RZT are derived by means of Hamilton's principle. The through-the-thickness variations of the transverse shear and normal stresses are calculated by integrating the stress equilibrium equations in a post-processing step. Therefore, the Peridynamic Least Squares Minimization (PDLSM) approach is utilized to obtain precise derivatives of axial stresses in the stress equilibrium equations. A new finite element formulation is built up with 3-nodes with a total of 15 DOF. In order to study the influence of transverse stretching, different types of boundary conditions and material variations are applied for laminated composite beams for the bending and free vibration analyses. The distribution of displacements as well as the axial and transverse stresses of the thick beams are extensively examined. The outcomes of RZT are in good agreement with the reference solutions in the literature. The findings of the present study reveal that the presence of the transverse stretching produces more realistic predictions for thick beams where the shear deformations are influential.