New Sinusoidal Higher-Order Theory Including the Zig-Zag Function for Multilayered Composite Beams

Abstract

With the advantage of satisfying zero shear stress conditions on surfaces, the sinusoidal theory has been widely used for static and dynamic analysis of composite laminated structures. Nevertheless, sinusoidal theories accounting for zig-zag effects have hitherto rarely been reported in the literature because zero shear stress conditions on the surfaces will be violated once the existing zig-zag function is taken into account. Thus, a new zig-zag function that can satisfy traction-free boundary conditions has been developed in this paper. Introducing the developed zig-zag function into the sinusoidal model, a new sinusoidal shear deformation beam theory including the zig-zag function has been proposed, which can accurately describe the zig-zag effect. Other higher-order theories and the first-order theory proposed by other investigators are also considered for the evaluation. By investigating the typical bending problems of multilayer beams, comparison of the present results with three-dimensional elasticity solutions and the results obtained independently using other models shows that the proposed model can more precisely produce the displacements and stresses of laminated composite and sandwich beams in comparison with other models considered in this article.