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

Abstract

International audienceThis 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 sta-tic 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 elas-ticity or finite element reference solutions in statics and vibration. Both convergence velocity and accu-racy are discussed. This finite element yields satisfactory results at a low computational cost

Static and free vibration analysis of laminated beams by refined theory based on Chebyshev polynomials

“…3 and the finite element expansion in Eq. 21, the previous relation can be rearranged as reported below (27) whereq sj indicates the nodal acceleration vector and M ijτ s indicates the fundamental nucleus of the element mass matrix, whose components are:…”

“…Murakami [25] introduced a zig-zag function into Reissner's new mixed variational principle. In [26], a refined sine model with Heaviside function for each layer was presented, whereas the sine model was improved by introducing Murakami's function in [27]. Onate [28] introduced a new linear two-node beam element based on the combination of Timoshenko and refined zig-zag kinematics.…”

Generalized Unified Formulation shell element for functionally graded Variable-Stiffness Composite Laminates and aeroelastic applications

“…Recently researchers [63,52,4,55,66] adopted Zig Zag models to solve various problems involving bending analysis of functionally graded sandwich structures, laminated beams, and buckling calculations. The effectiveness of taking into account the displacements' slope discontinuity at the interfaces with Zig Zag models was proven.…”

Free Vibration Analysis of Composite Laminated Beams

“…Polit [33]performed the vibration analysis of composite laminated beams by using the Murakami's zigzag function in the sine model. Vo and Thai [34] and [35] presented the free vibration of axially loaded composite beams with arbitrary lay-ups applying the parabolic shear deformation theory.…”