Mixed Finite-Element Formulation Based on Refined Sinusoidal Model for Buckling of Layered Beams

Abstract

In the last 3 decades, sinusoidal theory has been increasingly utilized to research mechanical behaviors of layered composite and sandwich structures. Nevertheless, the existing sinusoidal model will encounter trouble in precisely yielding the buckling loads of layered structures composed of layers with different material properties. Thus, a refined sinusoidal model is offered for the buckling analysis of composite and sandwich structures that can simulate the zigzag effect of the in-plane displacement and meet the free conditions of transverse shear stresses on the surfaces. In the light of the elegant sinusoidal model, a three-node beam element has been constructed to work out the discrete eigenvalue equation coming from the stability behavior. Making use of a mixed variational theorem from the literature, the finite-element formulation can meet beforehand the continuous conditions of transverse stress at the interfaces. The three-dimensional finite element method (3D-FEM) results are utilized to evaluate the precision and efficiency of the proposed approach through a numerical example. The proposed finite-element formulation can produce satisfactory results with lower calculational cost, and some interesting conclusions are presented. However, the results for stability of layered structures made of plies with different material properties will be overestimated by utilizing the models violating the continuous prerequisite of interlaminar stresses.