˺ ΔϴγΪϨϬϟ΍ ϡϮϠόϠϟ ϝϭϷ΍ ϲϤϴϠϗϹ΍ ήϤΗΆϤϟ΍ / ϦϳήϬϨϟ΍ ΔόϣΎΟ / ΔγΪϨϬϟ΍ ΔϴϠϛ ) ˾ - ˿ ϲϧΎΛ ϦϳήθΗ / ˻˹˹ ( Stress Analysis of Fiber-reinforced Composite Built-up Beam Using the Unit Cell Method Dr. Haydar A. Hussain Dr. Ala’a M. Hussain Luay M. Ali Babylon University Babylon University Babylon University College of Engineering College of Engineering College of Engineering Dept. of Materials Eng. Dept. of mech. Eng. Dept. of mech. Eng. Draletharihah@yahoo.com luya_m_63@yahoo.com ABSRACT Macro- and microscopic levels of analyses are used to capture the behavior of a built-in beam made of a unidirectional fiber-reinforced polymeric material. Finite element formulation based on the displacement approach and minimum potential energy principle is carried out in the longitudinal direction of the beam to determine the lateral displacements (deflections) at various sections, stresses and strains. A unit cell method in micromechanical analysis based on the finite element method is used to define the state and distribution of the stresses induced in transverse sections. Hexagonal fiber-matrix packing system is idealized for the problem. The package of ANSYS 5.4 and a Matlab v6.5 program are used to solve for the macro- and micromechanical analyses. To examine the validity of the presented method, it is applied to analyze a beam made of matrix and fibers with the same elastic properties. The results are then compared with those obtained using the method followed for isotropic materials considering the same values of the elastic properties , the convergence obtained verifies the validity of the analysis method adopted by the current work. ΔλϼΨϟ΍ : ϢΗ ΤΒϟ΍ ΍άϫ ϲϓ Κ ΠϤϟ΍ϭ ΔϴϧΎϴόϟ΍ ΔϴϜϴϧΎϜϴϤϟ΍ ΕϼϴϠΤΘϟ΍ ϡ΍ΪΨΘγ΍ ΓΩΎϣ Ϧϣ ΔϋϮϨμϣ ΔΒΘϋ ϙϮϠγ ΔόΑΎΘϤϟ ΔϳήϬ ΔϳήϤϴϟϮΑ ϑΎϴϟ΄Α Γ΍ϮϘϣ ϩΎΠΗϻ΍ ΔϳΩΎΣ΃ . ΎϴϧΪϟ΍ ΔϨϣΎϜϟ΍ ΔϗΎτϟ΍ϭ ΔΣ΍ίϹ΍ ϱ΃ΪΒϣ ϰϠϋ ΩΎϤΘϋϻΎΑ ΓΩΪΤϤϟ΍ ήλΎϨόϟ΍ ΔϘϳήσ ΖϣΪΨΘγ΍ ΪϳΪΤΘϟ ΕΎΣ΍ίϹ΍ Δϴοήόϟ΍ Ε΍ΩΎϬΟϻ΍ϭ ΕϻΎόϔϧϻ΍ϭ ϭ ϲϟϮτϟ΍ ϩΎΠΗϻΎΑ ΔϔϠΘΨϣ ϊσΎϘϣ ϲϓ ΎϨΜϧ΍ Ϧϣ ΔΠΗΎϨϟ΍ ΍˯ ΚΤΒϟ΍ ϊοϮϣ ΔΒΘόϟ . ΓΪΣϭ ϲΘϘϳήσ ΖϣΪΨΘγ΍ Δϴοήόϟ΍ ϊσΎϘϤϟ΍ ϲϓ ΔϧϮϜΘϤϟ΍ Ε΍ΩΎϬΟϻ΍ ϊϳίϮΗ ΔόϴΒσϭ ΔϴϋϮϧ ΪϳΪΤΘϟ ΓΩΪΤϤϟ΍ ήλΎϨόϟ΍ϭ ΔϴϠΨϟ΍ ΔΒΘόϟ΍ ϩάϬϟ . ΪϤΘϋ΍ ϮθΤϟ΍ ϡΎψϧ ϲγ΍Ϊδϟ΍ ϭ ϑΎϴϟϸϟ ΓΩΎϤϟ΍ αΎγϷ΍ ϟ ϖϴΒτΘϟ΍ ΍άϬ ϲΠϣΎϧήΑ ϝΎϤόΘγΎΑ ϞΤϟ΍ άϔϧϭ ) Ansys 5.4 & Matlab v6.5 ( δΤϟ ΏΎ Δϟ΄δϤϠϟ ΔϔϠΘΨϤϟ΍ Ε΍ήϴϐΘϤϟ΍ . ΔΒΘϋ ϞϴϠΤΗ ϢΗ ΔϴϟΎΤϟ΍ ΔϘϳήτϟ΍ ΔϴΣϼλ έΎΒΘΧϻϭ ΔόϨμϣ Δϴο΍ήΘϓ΍ Ϧϣ ϭ ϑΎϴϟ΃ ΓΩΎϣ αΎγ΃ ι΍ϮΨΑ ΓΪΣϮϣ Δϧϭήϣ ϊϣ ΎϬΠ΋ΎΘϧ ΖϧέϮϗϭ Ξ΋ΎΘϧ ΍ϮϤϟΎΑ ΔλΎΨϟ΍ ϕήτϟ΍ ΪϤΘϋ΍ ϞϴϠΤΗ ι΍ϮΨϟ΍ ΓΪΣϮϣ Ω ΔΒΘόϠϟ ι΍ϮΨϟ΍ Ε΍Ϋ ΩΎϤΘϋ΍ ϊϣ Δϴο΍ήΘϓϻ΍ ϨϴΑ ΏέΎϘΘϟ΍ ϥΎϛϭ ΔϴϟΎΤϟ΍ ΔϘϳήτϟ΍ ΔΤλ ϰϟ· ήϴθϳ ΎϤϬ . ϫ ΍ά ΏϮϠγ΃ ϲϓ ϊΒΘϣ Ϧϣ ήϴΜϜϟ΍ ωϮϨϟ΍ ΍άϫ Ϧϣ ΔϴϤϟΎόϟ΍ ΙϮΤΒϟ΍ . INTRODUCTION: The need to understand the composite materials drives the researches in this field into the micro-mechanics of this type of materials [1&2]. Theoretical and experimental methods are usually applied in micromechanical analysis in order to tackle such problems. The theoretical methods can be