### A Nonlinear Analytical Model for Symmetric Laminated Beams in Three-point Bending

*Youssef Benbouras, Aziz Maziri, Elhassan Mallil, Jamal Echaabi*

**Abstract**: The use of composite

materials with continuous fibers in the aircraft and aerospace industries

requires a thorough knowledge of behaviors of these laminate composites under

various loading conditions. Indeed, the aim of this work is to simulate linear and nonlinear

behavior of a symmetric laminated composite under three-point bending tests. The

modelization used is based on an analytical approximation that has been

recently developed for isotropic materials. This approximation is still valid

for the studied quasi-isotropic laminated composite because it is symmetric

with a specific layer sequence. The overall response of laminate composite is

determined from the behavior of each ply outside of their orthotropic axis. Two

methods are used to calculate the equivalent longitudinal Young-modulus of the

laminate. The result shows that when the deflection of the specimens is less

than 2.5 times the thickness, the difference between the experimental and

analytical curves is about 1% for the average global stresses method, and about

7.5% for the apparent bending modulus method. For large deflections, the

difference relative to the first method remains less than 11% and the second

method is about 20%.

**Keywords**: Analytical model; Graphite-epoxy composite; Large deflection; Linear and nonlinear behavior; Three-point bending test

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