A sine finite element using a zig-zag function for the analysis of laminated composite beams

摘要

This paper deals with the influence of the use of the Murakami's zig-zag function in the sine model for the analysis of laminated beams. The adding of this function introduces a discontinuity of the first derivative of the in-plane displacement with only one more unknown. The kinematics is based on a sine distribution and the transverse displacement remains constant through the thickness. The transverse shear strain is obtained using a cosine function avoiding the use of shear correction factors. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers. The purpose is to develop a finite element approach with a low computational cost and without numerical pathology. This study aims at determining the influence of an additional zig-zag function in the Sine model for static and vibration analysis. In this way, mechanical tests for thin/thick laminated and sandwich beams are presented in order to evaluate the capability of this finite element. The results are compared with elasticity or finite element reference solutions in statics and vibration. Both convergence velocity and accuracy are discussed. This finite element yields satisfactory results at a low computational cost.