Homogenization of Grewia Optiva Fiber Reinforced Epoxy Composite Using Higher Order Shear Deformation Theory

The present work proposes a computational procedure for evaluating the homogenized property of laminated composite plate. This type of model is beneficial for determining the basic mechanical properties of a laminated composite with significantly lesser computational effort. In this work a formulation is presented which is based on Reddy’s higher-order shear deformation plate theory which takes into account the effect of transverse shear deformation in composite laminates. This method is capable of finding equivalent homogenized properties for the laminated composite having any type of lamination scheme. Further this formulation is used to homogenized property of Grewia optiva fiber reinforced epoxy composite with different volume fraction and lamina scheme are calculated by using the proposed formulation. The accuracy and validity of the present computational algorithm is ensured by comparing the results with the available literature which provides good results.


Introduction
As the technology is growing demand for the composite material is growing continuously for the significant applications in the industries. In composite stress and strain varies 3-Dimensionally because of arbitrary orientation of fiber and various other factors, which makes the composite analysis difficult. An equivalent homogeneous model is used to overshoot this problem which can predict the overall behaviour of the laminated composite. This model can predict the equivalent mechanical properties of the composite which can be used further for any analysis. The homogenized model is used by the various researcher, Aref et al. [1] had homogenised (orthotropic Kirchhoff plate) the rib core sandwich panel. Some researchers have used equivalent homogeneous model for the analysis of sandwich panels with truss-core [2], corrugated core [3] and Z-core [4]. Nordstrand et al. have calculated transverse shear stiffness for different core configuration numerically as well as analytically [5]. While McCarthy [6]and Mandal [7] has used equivalent properties for bolt analysis.
A method is presented in this paper where equivalent homogenised properties are calculated by considering 3D elasticity of composite. Reddy's higher-order shear deformation theory (HSDT) [8] is used to homogenize the arbitrarily oriented lamina (i.e. non-homogenized) of the laminated plate. By using HSDT we have calculated the equivalent stiffness matrix which considers the effect of twisting, bending as well as shear stiffness which other theories exclude. A MATLAB program has been developed for this purpose. This MATLAB program is then used to calculate the Properties of Grewia optiva fiber reinforced epoxy composite with the fiber properties taken from Singha [9]. E E E As E2, E3 are transverse moduli, E3 can be found by using Eq. (13) for orthotropic lamina.

CS CS
Now the elastic properties can be obtained using a new compliance matrix as,

Properties of Grewia Optiva Reinforced Epoxy Composite
Now using the code, equivalent properties of Grewia optiva fibre reinforced composite material is calculated by using the properties of Fibre from Singha [8]. The properties are calculated by taking the fibre volume fraction as 0.4, 0.5 and 0.6. further two lay-ups are taken Quasi-isotropic layup and Zero-dominated layup.

Conclusion
• In this paper, a new 3D homogenizations method was proposed to calculate the properties of the laminated composite. • The approach can find the equivalent properties of any lamination scheme whether symmetric or asymmetric. • Using this method MATLAB code was develoded and used calculated the properties of composite. Further This code is validated through previous literature results which gives a well satisfactory result. • The present method is compared with the actual 3 D layered solid and with the result of Mandal paper by considering different lamination scheme. • Further properties of Grewia optiva fiber composite is calculated in this work.