Numerical Simulation on the Statics Deformation Study of Composite Cross Arms of Different Materials and Configurations

This study focuses on the deformation of cross arms made from composite material under static loading. Two materials properties of fiberglass with are assigned to the cross arms model and it is subjected to a load at the one end of the cross arms. A bracing support is then installed, and the deformation and stress experienced by the cross arms are observed and compared with the case where no bracing support is used. The results obtained show that material B has lower deformation value, but experienced greater stress compared to material A. The bracing managed to reduce the total deformation by about 12% and 20% for material A and B respectively. The reduction of stresses experienced by the cross arms ranges from 4% to 30%.


Introduction
Fiber-composite is one of the engineering material with high performance in terms of its strength and stiffness [1]. Fiberglass is one of the fiber-composite that is widely used. The applications of fiberglass ranges from food processing to power generation industries. This is due to its characteristic which it is easily moulded and shaped into complex forms. In the power generation industry, fiberglass was introduced as an insulation material for distribution and transmissions system as an additional component to the basic insulator [2]. Grzybowski and Disyadej [2] stated that the main reason is because fiberglass has high dielectric strength. In the case of fiberglass utilized in the distribution line pole, it is considered as a non-uniform composite material with fiber as the main element and resins and filers as the additional components [3]. In this study, the focus will be on the application of fiberglass in the cross arms of the transmission tower. Cross arms, one of many components that build the transmission tower, acts as a support to the transmission conductor [4]. It is constantly subjected to wind loads, its selfweight and other loads such as unexpected broken wire conditions, erections and maintenance [5]. Hence, the common materials used for the cross arms are wood, steel and fiberglass [4]. However, fiberglass is better because of its insulating characteristic and it has a greater mechanical strength to weight ratio, compared to the other two [4]. Therefore, this study aims at investigating the deformation of the composite cross arms under static loadings using finite element approach. A composite material for the cross arms with different material properties are tested in two different conditions, a cross arms without bracing support and a cross arms with a bracing support. The total deformation and stresses experienced by the cross arms will be evaluated and compared.

Finite element analysis (FEA)
Finite element method (FEA) is a numerical technique that benefitted from the computational power to obtain the approximation solutions of boundary value problems or field problems. The field is the domain that is represented by a physical structure. The field variables are the variables that governed by the differential equations and the boundary conditions are the values on the boundaries of the fields. The values of the field variable calculated at the nodes are used to determine the values at non-nodal points by means of interpolation. For a three-node triangle example, the field variable can be represented such as: ( , ) = 1 ( , ) 1 + 2 ( , ) 2 + 3 ( , ) 3 (1) Where 1 , 2 and 3 are the values of the field variable at the nodes, 1 , 2 and 3 are the interpolation functions. This Eq.1 is also known as the shape function.

Shell element
Shell elements are suitable to model thin structures. Thin structure denotes a geometry where one dimension is so small compared to the other two dimensions. Shell elements separate the deformation on the surface and in the normal direction, hence simplify and creating a more efficient simulation. It is usually done by meshing the surface that representing the structure and providing the section data to create the shell thickness. There are three assumptions to be made when implementing the shell element: (1) stresses are assumed to be linear through the thickness; (2) the center surface does not experience any bending and (3) the membrane stresses are uniform over the thickness. For this simulation, the thickness to be associated with the 3D model is 6 mm. It is set in the ANSYS ACP model setup. The 6 mm thickness later is divided and oriented according to the composite material as stated in Table 2.

3-D model
Each cross arm was designed and assembled using SOLIDWORKS 2017 software. Figure 1 (a) shows the cross arms design while Figure 1 (b) shows the cross arms with a bracing installed to the four arms. The material properties for the cross arms were later assigned in ANSYS ACP.

Material properties
Two composite material properties, A and B are assigned to the cross arms as tabulated in Table 1. Besides that, the material A is made to be only five layers of composite material while material B is made to have nine layers of composite material. Table 2 shows the fiber orientation and thickness for each layer of the material A and B.

Boundary conditions (BCs)
For the simulation, a couple of BCs have been assigned to the cross arms model. Each ends of the cross arms leg is assigned with a fixed support, as shown in Figure 2 (a). The load is applied to the top end of the cross arms as in Figure 2

Maximum deformation
The total deformations and stresses experienced by the cross arms for material A and B, with and without bracing are tabulated and presented in this section. Table 3 is the total deformation experienced by the cross arms for material A and B, with and without the support of the bracing. The deformation distribution of both cases in each material is similar, where the maximum deformation happens in the region where the load is applied and the minimum deformation occurs in the region where the fixed supports are applied.
For material A, the maximum deformation of the cross arms without the bracing support is around 127 mm, and it is located near the region where the load is applied. However, with the support of the bracing, the maximum deformation managed to be reduced to 111 mm, a reduction of 12%. For material B, the maximum deformation of the cross arms for the standard case is 79 mm, while the case where the bracing is installed is 63 mm. A decrease of 20% in maximum deformation is obtained for the material B. This results shows that the installation of bracing is capable of reducing the maximum deformation experienced by the cross arms.
As for the comparison between material A and B, material B experienced a lower maximum deformation for both cases (standard: 79 vs. 127 mm; bracing: 63 vs. 111 mm). Table 4 shows the total deformation contour for material A and B for the case of with and without bracing.  Table 4. Comparison of deformation experienced by different material for cross arm with and without bracing.

Deformation Standard Bracing
Material A Material B

Maximum stress
The maximum stress for material A and B for cases of with and without bracing support are recorded in Table 5 and 6 respectively. Each layer experienced different stress magnitude and the presence of bracing reduced the stress exerted to the cross arms for both materials. In material A, the used of bracing lower the maximum stress value more than 5% in each layer. The highest reduction achieved is at layer 3, where the maximum stress obtained before and after the placement of bracing is 178.30 MPa and 124.58 MPa respectively, a reduction of approximately 30%. A similar observation is recorded for material B, where the bracing support reduced the maximum stress subjected to the cross arms with a reduction of more than 5%. The maximum reduction achieved is at layer 5, where the maximum stress obtained before and after the placement of bracing is 153.84 MPa and 143.36 MPa respectively, a reduction of 6.81%. For the comparison between material A and B, material B seems to be experiencing greater maximum stress compared to material B, as tabulated in Table 5 and 6. Figure 3 shows the plotted maximum stress for material A and B in each layer. The maximum stress experienced at each layer seems to be lower for the layer close to the center and higher at the outer layer of the material. The distribution of stress for both materials for each case seems to be similar where the maximum stress recorded is in the tip region of the cross arms. Figure 4 shows the stress distributions at layer 1 for material A for case of without and with bracing. The distributions of stress in each layer is also similar, in both material, for both cases. Hence, for simplicity, only layer 1 of material A is included in this paper.

M A T E R I A L B
Without bracing With bracing