Stability of laminated composite and sandwich beams by a Reddy-type higher-order zig-zag theory

Abstract

ABSTRACTTransverse shear stresses have a significant influence on the buckling analysis of laminated structures. Thus, the models violating interlaminar continuity of transverse shear stress will encounter difficulty for the buckling analysis. The postprocessing method by integrating three-dimensional equilibrium equation is also invalid, as the transverse shear stresses obtained from the postprocessing method are unable to be involved in the strain energy. In this paper, a Reddy-type higher-order zig-zag theory is firstly proposed, in which the in-plane displacement field is obtained by superposing the developed zig-zag function on the displacement field of Reddy's theory. To predict accurately the buckling behaviors of laminated composite and sandwich beams, a new equilibrium approach in conjunction with the Hu-Washizu (HW) mixed variational principle has been developed to produce the improved transverse shear stresses. Moreover, the accurate transverse shear stresses can be involved in the strain energy which can actively impact the accuracy of buckling stresses. To assess the performance of the proposed method, the critical loads of the laminated composite and sandwich beams with various configurations have been analyzed. Agreement between the present results and the solutions of layerwise are very good, and the proposed model only includes the four displacement parameters which can illustrate the accuracy and effectiveness of the present model. In addition, new results using all the models considered in this paper have been presented which can serve as a reference for future investigations.