This paper focuses on some mathematical and numerical aspects of elastic stress. The distribution of elastic stress in rotating cylinders made of Boron carbide (B4C) and Silicon carbide (SIC) materials is analyzed analytically. Boron carbide, which will be Decelerated for projects in the defense industry and automotive fields, is among the precious metals in the world. Silicon carbide is one of the most widely used structural ceramics. silicon carbide is one of the most durable ceramic materials. Boron carbide (B4C) and Silicon carbide (SIC) are used in aircraft industry, unmanned aerial vehicles, electric vehicles. The stress value obtained at the end of the analysis was compared with the ANSYS 2023 R1 program. The results obtained are close to each other. For example, if the results obtained are compared with each other, the tangential stress obtained in the boron rib material is about 35\% higher than that of silicon carbide. The novelty and importance of the research are quite high. Rotating cylinders determined materials are used in aircraft, unmanned aerial vehicles.
It is intended to share the results obtained when using two materials with high strength with the literature. The radial stresses are continuously zero at the innermost and outermost parts. Tangential stresses are more than radial stresses. It has been observed that the tangential stresses obtained in the ANSYS 2023 R1 program are higher than the radial stress. Within the scope of the study; the Von Mises yield criterion is taken into account in the plane shape change reference. 
The findings obtained at the end of the study are shared in graphs. At the end of the study, it is determined that the stresses occurring in the cylinder with silicon carbide (SIC) material were more than Boron carbide (B4C). Moreover, the results are compared among themselves

Hüseyin Fırat KAYIRAN

Ulviye DEMİRBİLEK

English

ZENODO

Asia MathematikaVolume: 7 Issue: 2 , (2023) Pages: 84 – 56Available online at www.asiamath.orgInvestigation of stresses occurring in rotating cylinders made of Boron carbide(B4C) and Silicon carbide (SIC) materials by using finite element methodHüseyin Fırat KAYIRAN1∗and Ulviye DEMİRBİLEK21Agriculture and Rural Development Support Institution (ARDSI),Mersin, TURKEY. ORCID iD: 0000-0003-3037-52792Department of Mathematics, Mersin University,Mersin, TURKEY. ORCID iD: 0000-0002-5767-1089Received: 19 Jul 2023 • Accepted: 02 Aug 2023 • Published Online: 31 Aug 2023Abstract: This paper focuses on some mathematical and numerical aspects of elastic stress. The distribution of elasticstress in rotating cylinders made of Boron carbide (B4C) and Silicon carbide (SIC) materials is analyzed analytically.Boron carbide, which will be Decelerated for projects in the defense industry and automotive fields, is among the preciousmetals in the world. Silicon carbide is one of the most widely used structural ceramics. silicon carbide is one of themost durable ceramic materials. Boron carbide (B4C) and Silicon carbide (SIC) are used in aircraft industry, unmannedaerial vehicles, electric vehicles. The stress value obtained at the end of the analysis was compared with the ANSYS2023 R1 program. The results obtained are close to each other. For example, if the results obtained are compared witheach other, the tangential stress obtained in the boron rib material is about 35% higher than that of silicon carbide.The novelty and importance of the research are quite high. Rotating cylinders determined materials are used in aircraft,unmanned aerial vehicles. It is intended to share the results obtained when using two materials with high strength withthe literature. The radial stresses are continuously zero at the innermost and outermost parts. Tangential stresses aremore than radial stresses. It has been observed that the tangential stresses obtained in the ANSYS 2023 R1 programare higher than the radial stress. Within the scope of the study; the Von Mises yield criterion is taken into account inthe plane shape change reference. The findings obtained at the end of the study are shared in graphs. At the end ofthe study, it is determined that the stresses occurring in the cylinder with silicon carbide (SIC) material were more thanBoron carbide (B4C). Moreover, the results are compared among themselves.Key words: finite element method, Mathematical modeling, Elastic stress distribution, Boron carbide (B4C), Siliconcarbide (SIC).1. IntroductionThe innovation of this study is very important from an engineering point of view. Rotating wipers are often usedin machine parts in the air industry. The stress behavior of two different materials has been investigated. Inaddition, studies carried out to understand this issue have been investigated in detail. In this context, the effectof poisson’s ratio on functionally graded pressure vessels was investigated in a study [1].In another study; thestresses occurring in hollow cylinders with FGM material were investigated. The radial and tangential stressesobtained at the end of the study were revealed separately. They have revealed the importance of the design ofhollow cylinders [2, 3]. The stresses occurring in isotropic cylinders are shared as a table [4].In a different study, the stresses and displacements in spherical shells made of functionally graded material©Asia Mathematika, DOI: 10.5281/zenodo.8369150∗Correspondence: huseyinfiratkayiran@gmail.com84Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEKsubjected to internal and external pressure were calculated and the results obtained were shared with theliterature [5]. Elastic stresses in hollow cylinders and spheres were investigated by thermal stress analyses ofa disk subjected to mechanical load and linearly increasing temperatures in [6, 7]. In other study, the stressesoccurring in the FGM hollow disk and cylinder subjected to homogeneous internal pressure were examined [8].Finite element method is the use of calculations, models and simulations to understand how an objectmay behave under various physical conditions. This method have been used recently to many problems severalapplied fields, such as engineering mechanics [9, 10], mathematics [11] and others [12, 13].Different studies contributing to materials science were given respectively; Carbon laminated compositeand e-glass epoxy rotary brake discs, Glass fiber reinforced polymer composites: short characterization ofmechanical and thermal properties of natural fiber reinforced thermoplastic composites and improvement ofwear behavior of epoxy resin with boron carbide reinforcement were investigated. The results obtained areshared with the graphs [16, 17]. In one of the studies, thermal stresses were investigated in composites withthermoplastic materials. In addition, in a different study, the mechanical functions of boron carbide materialwere investigated [18, 19].It is very important to examine the elastic stresses that occur in machine parts using with this knownmethod. Cylinders are also preferred in the field of engineering and heavy industry. Rotating cylinders are alsofrequently used in unmanned aerial vehicles, airplanes and the aerospace industry. In this study, two differentmaterial cylinders were determined in this context. The differences between the obtained elastic stresses weredeciphered.1.1. ExperimentalIn this section, each method is discussed in detail and step by step. It is given how these methods calculate thetemperature distribution of cylinders with rotating Boron carbide (B4C) and Silicon carbide (SIC) materials.The angular velocity of the cylinder is determined as 50 rad / s. According to the analytical and FEM testresults, the results of elastic stress were obtained. Three different methods are given: (i) finite element program(Ansys 2023 R1), (ii) analytical solution (mathematical modeling) and (iii) our results are compared with otherstudies in the literature.1.2. ANALYTICAL SOLUTIONThe inner radius and outer radius of the cylinder are respectively determined as 50 mm and 100 mm.Themechanical properties of boron carbide and silicon carbide cylinders to be analyzed are given in Table 1 belowTable 1. Displacements in the radial direction occurring inside the discs.No E (Gpa) Density (kg/m3) Inner half diameter(mm) Outer semi-diameter(mm)1 460 2520 50 1002 480 3210 50 1001.3. Stress analysis in cylindersThe boundary layer on a rotating cylinder with axial flow is shown in Figure 1.The two-dimensional equilibrium equation in cylindrical coordinates is derived from the reference [15]and the following equations are derived. Stresses were determined in radial and tangential directions. A is acoefficient, where C1 and C2 are integral constants.85Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEKFigure 1. Boundary layer on a rotating cylinder with axial flow [14]F = C1r(n+k)/2 + C2r(n−k)/2 +A(3+gama)r (1)It is obtained. Radial and tangential stresses,σr = C1r(n+k−2)/2 + C2r(n−k−2)/2 +A(2+gama)r (2)σθ = (n+ k)/2C1r(n+ k − 2)/2) + (n− k)/2C2r((n− k − 2)/2) + (3 + gama)Ar(2 + gama) + (P (r)w2r2) (3)1.4. Results and discussionTable 2. Stresses occurring in the cylinderSurface n TangentialStress(Mpa)ANSYS 2023 Axialstress(Mpa)RadialStress(Mpa)In (B4C) n=-1 770,067 769,052 260,00 0Outside (B4C) n=-1 119,155 117,275 40,235 0In (SIC) n=-1 575,54 574,00 189,42 0Outside (SIC) n=-1 89,059 88,77 29,309 0In (B4C) n=-0,5 555.618 556,013 180,00 0Outside (B4C) n=-0,5 85,972 83,714 29,026 0In (SIC) n=-0,5 415,266 418,993 131,136 0Outside (SIC) n=-0,5 64,258 62,007 21,148 0In (B4C) n=0 380.16 376,146 135,00 0Outside (B4C) n=0 60,335 19,860 43,966 0In (SIC) n=0 284,130 285,118 127,62 0Outside (SIC) n=0 43,966 44,747 14,469 0In (B4C) n=0,5 272.17 85,00 203,818 0Outside (B4C) n=0,5 42,195 41,247 14,246 0In (SIC) n=0,5 203,818 201,885 98,352 0Outside (SIC) n=0,5 31,538 30,975 11,379 0In (B4C) n=1 190,08 188,44 69,00 0Outside (B4C) n=1 29,411 26,040 9,931 0In (SIC) n=1 142,065 140,112 50,424 0Outside (SIC) n=1 21,983 20,552 7,235 086Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEKThe inner half diameter of the modeled cylinder is 50 mm and the outer half diameter is 100 mm.One ofthe cylinders was selected as Boron carbide (B4C) material. The material of another cylinder was determinedto be Silicon carbide (SIC). At the end of the literature review, it was understood that Boron carbide (B4C)and Silicon carbide (SIC) material cylinders can be used today. Radial, tangential, axial and equivalent stressdistributions were formed in cylinders consisting of hollow cylinders of two different materials subjected toangular velocity during rotation.It has been determined that the radial stress distributions in the inner andouter parts of the cylinders are zero. The tangential stresses show a decreasing distribution from the innerto the outer part of the cylinder. It occurs at the largest value of the rating parameter of the most regulardistribution. the stresses formed in hollow cylinders subjected to an angular velocity of 50 rad/s are givenin Figure 1-6 below. In Table 2, stress values of bronze and titanium material cylinders exposed to differentangular velocities are given.In Figure 2 below, radial stresses occurring in a titanium material cylinder rotating at an angular velocityof 50 rad/sec are given.Figure 2. Radial stresses occurring in an angular (50 rad/sec) rapidly rotating Bor karbür (B4C) material cylinder.In Figure 3 below, radial stresses occurring in Silicon karbür (SİC) material cylinder rotating at anangular velocity of 50 rad/sec are given.Figure 3. Radial stresses occurring in an angular (50 rad/sec) rapidly rotating Silicon karbür (SİC) material cylinder.In Figure 5 below, the tangential stresses occurring in a Silicon karbür (SİC) material cylinder rotatingat an angular velocity of 50 rad/sec are given.87Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEKFigure 4. Tangential stresses occurring in an angular (50 rad/sec) rapidly rotating Bor karbür (B4C) material cylinder.Figure 5. Tangential stresses occurring in an angular (50 rad/sec) rapidly rotating Silicon karbür (SİC) materialcylinder.In Figure 6 below, axial stresses occurring in a titanium material cylinder rotating at an angular velocityof 50 rad/sec are given.Figure 6. Angular (50 rad/sec) rapidly rotating titanium Bor karbür (B4C)material in the cylinder that occurs axialstresses.In Figure 7 below, axial stresses occurring in a Bor karbür (B4C) material cylinder rotating at an angularvelocity of 50 rad/sec are given.In Figure 8-10 given below, the nodal points of the cylinder were modeled in the ANSYS 2023 R1 program88Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEKFigure 7. Angular (50 rad/sec) rapidly rotating Silicon karbür (SİC) material in the cylinder that occurs axial stresses.and determined. In addition, the force applied to the cylinder is revealed.Figure 8. Entry of the cylinder dimensions into the ANSYS 2023 R1 program.Figure 9. Modeling of the cylinder with ANSYS 2023 R1 program.89Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEKFigure 10. Detection of nodal points in the cylinder.2. ConclusionIn this study, the stresses occurring in hollow cylinders rotating with Boron carbide (B4C) and Silicon carbide(SIC) materials were investigated. The results obtained were compared among themselves. Dec. As a result ofthe researches, the radial stresses in the innermost and outermost parts of the cylinders are zero.It is inversely proportional to the increase of the rating parameter of the stresses in the cylinders.The tangential stresses occurring in the inner part of the silicon carbide (SIC) cylinder are approximately33.79% greater than the stresses occurring in the Boron carbide (B4C) cylinder when n = -1 and w = 50 rad/s;The axial stresses occurring outside the silicon carbide (SIC) cylinder are approximately 37.26% greaterthan the stresses occurring in the Boron carbide (B4C) cylinder when n = -1 and w = 50 rad/s; It was determinedthat the radial stresses were higher in the Silicon carbide (SIC) cylinder than in the cylinder with Boron carbide(B4C) material.It has been observed that the numerical results obtained and the analytical results obtained with theANSYS 2023 R1 program show similarities with each other. It is thought that the difference between numericaland analytical results is around 3% maximum, which can be considered as an excellent result.AcknowledgmentI would like to express my gratitude to our family who did not spare their moral support during our studies.References[1] Eker M, Semipabuc D. Generalized Thermoelastic Behavior of an Isotropic Hollow Cylinder, Turkish Journal ofNature and Science, 2022; 1:123-128.[2] Holder N, Öztürk M. Precise solutions for stresses in functional grade pressure vessels. Composites Part B: Engi-neering, 2001; 32:683-686.[3] Bosphorus C. Elastic Analysis of a Hollow Cylinder Made of Functional Grade Material Subjected to InternalPressure, International Scientific and Professional Studies Journal, 2018; 2:56-66.[4] Horgan CO, Chan AM. The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded isotropic LinearElastic Material, Journal of Elasticity,1999; 55:43-59.90Hüseyin Fırat KAYIRAN and Ulviye DEMİRBİLEK[5] Nejad MZ, Abedi M, Lotfian MH, Ghannad M. A Definitive Solution for Stresses and Displacements of PressurizedFGM Thick-Walled Spherical Shells with Exponentially Varying Properties”, Journal of Mechanical Science andTechnology, 2012; 12: 4081-4087.[6] Obata N, Noda N. Constant thermal stresses in a hollow circular cylinder and a hollow sphere of a functionallygradiated material. Journal of thermal stresses, 1994; 17:471-487.[7] Nie GJ, Batra RC. Stress analysis and material adaptation in isotropic linear thermoelastic incompressible func-tionally graded rotating disks of variable thickness. Composite Structures, 2010; 92:720-729.[8] Peng Xu-Long, Li Xian-Female. The effects of gradient on stress distribution in rotating functionally graded soliddisks. J of Mechanical Science and Technology, 2012; 26:1483–1492.[9] Kayiran HF.Numerical analysis of composite disks based on carbon/aramid epoxy materials. Emerging MaterialsResearch, 2022; 11: 155-159 .[10] Uçar M, Kayiran HF, Korkmaz AV. Gamma Ray Shielding Parameters of Carbon-Aramid/Epoxy Composite.Emerging Materials Research, 2022; 11: 338-344.[11] Bulut H, Aktürk T, Uçar Y. The Solution of Advection Diffusion Equation by the .Finite Elements Method,International Journal of Basic Applied Sciences, 2013; 13:88-97.[12] Biswal K, Bhattacharyya S. Dynamic response ofstructure coupled with liquid sloshing in a laminated com-positecylindrical tank with baffle.Finite Elements in Analysisand Design, 2010; 11:966–981.[13] Biswal K, Bhattacharyya S, Sinha P. Dynamic response analysis of a liquid-filled cylindrical tank with annularbaffle. J of Sound and Vibration, 2004; 1:13–37.[14] Melikhov IF, Chivilikhin SA, Popov IY. Flow on the surface of sloped rotating cylinder. Zeitschrift für angewandteMathematik und Physik,2020; 4:1-1.[15] Timoshenko SP, Goodier, J.N. Theory of Elasticity, 3rd Edition, McGraw Hill, New York, 1970.[16] Kayıran HF. Rotating brake discs with carbon laminated composite and e-glass epoxy material: a mathematicalmodeling. I Polymer Journal, 2023; 4:457-468.[17] Sathishkumar TP, Satheeshkumar S, Naveen J. Glass fiber-reinforced polymer composites: A review. J. Reinf PlastComposites, 2014; 33:1258-1275.[18] Kısmet Y, Dogan A.Characterization of the mechanical and thermal properties of rape short natural-fiber reinforcedthermoplastic composites. I Polym Journal, 2022; 31:14-.[19] Tasyurek M, Duzcukoglu H. Improving the wear behavior of epoxy resin with boron carbide reinforcement. I PolymJournal, 2022; 31:169-184.91

Investigation of stresses occurring in rotating cylinders made of Boron carbide (B4C) and Silicon carbide (SIC) materials by using finite element method

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Investigation of stresses occurring in rotating cylinders made of Boron carbide (B4C) and Silicon carbide (SIC) materials by using finite element method

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