Linear static, geometric nonlinear static and buckling analyses of sandwich composite beams based on higher-order refined zigzag theory

This study aims at developing finite element formulations based on higher-order refined zigzag theory (HRZT) to analyze sandwich composite beams under linear static bending, geometric nonlinearity and buckling. In HRZT, the higher-order terms associated with average shear strain and rotation due to zigzag are added based on refined zigzag theory (RZT). In linear static bending analysis, both C⁰ and C¹ elements are developed. For the C⁰ element, an extra node is used in order to eliminate shear locking. For geometric nonlinear static analysis, the two-node C⁰ element is developed to solve the bending response with lateral loading and buckling response. The numerical results are compared with those calculated by 2D exact solutions, analytical solutions of HRZT and 2D models using commercial software. Various beam theories such as first-order shear deformation theory (FSDT), higher-order shear deformation theory (HSDT), RZT, and other types of higher-order zigzag theory are also introduced for comparisons. Through comprehensive comparisons with existing works on FEM or zigzag theories, the HRZT beam elements developed in this study exhibit superior accuracy and are free from shear locking in linear static analysis. Furthermore, the study also demonstrates that these elements achieve high accuracy in geometric nonlinear analysis and buckling analysis.