Designing Cantilever Models from Various Materials and Comparing Them When They are under Constant Load and Have Holes

Subsequently the turn of the 20th century, composite materials have gained popularity. This new class of material has subsequently surpassed metals in a number of application areas [1, 2]. The advantage of these materials is the ability to customize the resin formulation or the reinforcements based on the environment the component will be used in [3].

The creation of high-performance fibers like Kevlar, glass, and carbon fibers has made a substantial contribution to the advancement of composite materials. Space, aviation, sports, and the military are just a few industries that use Kevlar/Epoxy composite materials [4-6].

Lateral-torsional buckling (LTB), a frequent global instability event for thin structures, occurs when the external load reaches the critical value and materials bent in the plane of highest flexural stiffness bow laterally and torsionally. Since a beam's flexural stiffness in the plane of bending is larger than its lateral rigidity, LTB must be taken into account while constructing the beam. As a result, in addition to deformation and stress calculations, the limiting load of LTB must be considered during the engineering design process [7, 8].

Buckling deformation is more complicated for steel cantilever beams because of the properties of the boundary condition. In contrast to merely supported beams, cantilevers have maximum displacement and rather than close to the mid-span, the torsion angle is at the free end [9]. In addition to researching cantilever beams and standard simply supported beams, many researchers also took into account additional elements like pre-stressed beams, material properties, early defects, and flange-web interaction [10, 11].

In engineering applications, thin-walled box-beam constructions composed of composite materials are frequently employed, for example as the arms of robots, antenna supports, helicopter blades, or airplane wings. They can have their characteristics altered throughout the fabrication process and are lightweight materials. Particularly for applications like as active vibration control and health monitoring, it is crucial to accurately characterize their dynamical features [12-14].

In the industrial domains, composite materials have grown significantly in importance. One of the most popular composite kinds is the sandwich construction. They typically consist of two robust, thin face sheets (skins), which are sandwiched together by a light core. When joined to form a sandwich panel, the core and skins which are typically flexible and weak create a robust and light-weight structure [15-17]. Composite structures are put under a variety of loading situations, including tensile, flexural, torsion, and fatigue, among others. Construction and transportation sectors frequently use cantilever beam structures with end loads or distributed loads. The cross section of the composite cantilever constructions is typically produced with a constant value along the axis of the beam. Structure shape optimization aids in identifying the shape that is ideal in that it reduces a particular cost function while meeting predetermined limits [18, 19].

In order to find engineering materials that are lightweight and environmentally friendly, a lot of research has compared the use of traditional and modern composite materials in a variety of engineering applications and in a wide range of fields, including aviation, ships, buildings, construction, and the manufacture of various mechanical parts used in laboratories, factories, car companies, trains, etc. It is less expensive to produce than conventional materials, and these research [20-27] are the most significant.

The analysis of arbitrary geometries and loading conditions can be done generally using numerical methods. Finite Element Analysis (FEA), one of the numerical techniques, has been successfully used in a wide range of applications; however, this type of analysis necessitates the generation of a sizable dataset in order to obtain results that are reasonably accurate, and it requires a significant investment of engineering time and computer resources [28].

FEA is reliant on engineering analysis in mechanical engineering applications and uses it to provide accurate solutions through mathematical equations and operating procedures that connect it directly to computers [29].

In this paper, On the surfaces of various holes, four cantilever models will be created, and the finite element technique will be used through the use of ANSYS software to recognize the behavior and resistance of each model under the influence of an external curvature load, projected at the end of each model. Each model will be made of different materials, and these materials will be made of steel and different composite materials. The steel model will be compared with the other three models made of different composite materials, in terms of stresses, strains, displacements and deformations that appear on the four models after loading. Additionally, a nine-point path will be chosen starting from the beginning of the models, passing through the holes at the bottom of the models' surfaces, and ending at the end of the models, comparison of the behavior and resistance of the four models at these holes when they are subjected to an external bending load.

The testing involved using four distinct kinds of materials. The following materials are employed, listed in order of importance: Steel, aramid fiber reinforced composites with epoxy matrix, glass fiber reinforced composites with epoxy resin matrix, and carbon fiber reinforced composites with epoxy matrix. Both PAN-based carbon fiber from Zoltek Corporation in the USA and e-glass fiber from PPG Ind., Inc. in the USA are used. Table 1 presents the mechanical characteristics of the fibers. In this investigation, the matrix was made of epoxy resin and two different hardener types.

The mechanical properties of the steel, epoxy resin, and carbon fiber composition in Table 1 should be described. Table 2 shows the findings of the mechanical characteristics of the composite materials as determined by the Mathcad-15 program. Table 3 lists the models, codes, particular disciplines, element kinds, and load types applied by the ANSYS 15.0 program.

Table 1. It displays the mechanical characteristics of the different composite fibers, as well as the bonding material consisting of the epoxy resin [30-33]

Table 2. The mechanical characteristics of composite materials produced by the software Mathcad 15

Table 3. The ANSYS 15.0 program uses models, codes, individual disciplines, element types, and load types

Micromechanical models were used to predict the elastic properties of three thermoplastic materials: carbon fiber, aramid fiber Kevlar-49, and glass fiber with a fiber content of up to 55%. These materials were then tested using the finite element method in the ANSYS program. Following conclusions were drawn from the study results:

• The deflection results values in composite models is more than the deflection in steel, which was (8.791 mm) in steel model, according to the data. Whereas it grew by (159.072%) in the carbon fiber model, it increased by a greater amount and reached (330.627%) in the carbide fiber model, while in the glass fiber model, it increased by the highest increase, as it increased by (459.675%) of the deflection values in steel.
• Nearly at the same rates as the increase in deflection in composite material models, the displacements (${{U}_{x~,}}{{U}_{y~,}}{{U}_{sum~}}$), also increased in comparison to the values of the displacements (${{U}_{x~,}}{{U}_{y~,}}{{U}_{sum~}}$) in the steel model.
• The stresses results, it can be concluded that the maximum normal stresses (${{\sigma }_{x}}$) in the composite material models are lower than those in the steel model. Whereas the percentage decline in the second model was (33.2%), it decreased by (33.28%) in the third model, and by (33.32%) in the fourth model. In comparison to the first model, the values of the maximum normal stresses (${{\sigma }_{y}}$) in the second, third, and fourth models were each somewhat lower (7.61%, 7.65%, and 8.34%) respectively. Maximum shear stress (${{\tau }_{xy}}$) values in composite models increased proportionally when compared to the steel model, rising in the second model by (36.34%), the third model by (36.4%), and the fourth model by (36.29%). The results from the calculation of the maximum stress intensity (${{\sigma }_{int.}}$) indicate that the values of the second, third, and fourth models, which are made of various composite materials, are lower than those of the first model, which is made of steel, with proportions of (33.34%, 33.41%, and 33.44%), respectively.
• The values of various strains ($\varepsilon_x,\ \varepsilon_y,\ \varepsilon_z,\ \varepsilon_{x y},\ \varepsilon_{\text {int.}}$) for the three models constructed of various composite materials rise relative to the steel model and vary in the following forms:

$\left(\varepsilon_{x 2}=61.47 \% ;\ \varepsilon_{x 3}=76.73 \% ;\ \varepsilon_{x 4}=82.07 \%;\right.$

$\varepsilon_{y 2}=75.61 \%;\ \varepsilon_{y 3}=81.13 \%;\ \varepsilon_{y 4}=81.13 \%;$

$\varepsilon_{z 2}=42.86 \%;\ \varepsilon_{z 3}=67.41 \%;\ \varepsilon_{z 4}=75.82 \%;$

$\varepsilon_{x y 2}=83.46 \%;\ \varepsilon_{x y 3}=89.94 \%;\ \varepsilon_{x y 4}=92.18 \% ;$

$\left.\varepsilon_{\text {int. } 2}=61.21 \%;\ \varepsilon_{\text {int. } 3}=76.29 \%;\ \varepsilon_{\text {int. } 4}=81.62 \%\right).$

• The results of displacements, stresses and strains at the seven points (2, 3, 4, 5, 6, 7, 8) located on the holes on the path ( A - A), show that the highest values were recorded in the following points: in the third point the highest values (${{\sigma }_{x~,~~}}~{{\tau }_{xy~,~~}}{{\sigma }_{int.~,~~}}~{{\varepsilon }_{x~,~~}}~{{\varepsilon }_{y~,~~}}{{\varepsilon }_{z~,~~}}~{{\varepsilon }_{xy~,~~}}~{{\varepsilon }_{int.~,~~}}$), in the fourth point the highest values were (${{\sigma }_{y}}$), and the highest values were recorded in the fifth point (${{U}_{x~~}}$), while on the eighth point the highest points (${{U}_{y~}},~{{U}_{sum~}}$).