Non-uniform Porosity Distribution on a Hollow Cylinder with Thermo-magnetic Mechanical Loading

Tantawy, Rania M.; Alghamdi, Mohammed A.; Zenkour, Ashraf M.

doi:10.22055/jacm.2024.47920.4842

Non-uniform Porosity Distribution on a Hollow Cylinder with Thermo-magnetic Mechanical Loading

Document Type : Research Paper

Authors

Rania M. Tantawy ¹

Mohammed A. Alghamdi ²

Ashraf M. Zenkour ² ^{, 3}

¹ Department of Mathematics, Faculty of Science, Damietta University, P.O. Box 34517, Egypt

² Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

³ Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt

10.22055/jacm.2024.47920.4842

Abstract

Currently, with the tremendous development in manufacturing composite materials, porous functionally graded materials have attracted many engineering, thermal, and electrical studies and applications on porous structures as most recent applications in functionally graded (FG) materials. In this study, semi-analytical solutions are investigated for perfect and porous FG hollow cylinders influenced by magnetic, and thermo-mechanical loads. Porosities with random distribution on the cylinder are considered. Magneto-thermo elastic characteristic of porous FG cylinder is substantive by modulated power law for even and uneven distributions of porosity in a radial direction of a porous hollow cylinder. The contribution of the present paper is demonstrated in providing complete elastic solutions for porous FG cylinders by considering perfect, even, and uneven distribution. Also, the validation of the grading index and porosity factor on the porous cylinder is reported for two different cases of boundary conditions. All of the two cases are studied in detail and the results of comparison between perfect and porous material are tabulated and discussed. The conclusion of this study should assist with developing mechanical engineering applications.

Keywords

Porosity

Hollow cylinder

Magnetic field

Temperature

Semi-analytical solution

Functionally graded

Subjects

Composite/Smart Materials

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Xu, Q., Ma, A., Saleh, B., Li, Y., Yuan, Y., Jiang, J., Ni, C., Enhancement of strength and ductility of SiCp/AZ91 composites by RD-ECAP processing, Materials Science and Engineering: A, 771, 2019, 138579.

[2] Li, W., Han, B., Research and application of functionally gradient materials, IOP Conference Series: Materials Science and Engineering, 394, 2018, 1–7.

[3] Saleh, B., Jiang, J., Ma, A., Song, D., Yang, D., Xu, Q., Review on the influence of different reinforcements on the microstructure and wear behavior of functionally graded aluminum matrix composites by centrifugal casting, Metals and Materials International, 26, 2020, 933–960.

[4] Tarlochan, F., Functionally graded material: a new breed of engineered material, Journal of Applied Mechanical Engineering, 1(5), 2012, 1-5.

[5] J Xie, P Shi, F Li, Exact solutions for the symmetric elastoplastic response of functionally graded pressure vessels, Thin-Walled Structures, 192, 2023, 111165.

[6] Saadatfar, M., Zarandi, M.H., Effect of angular acceleration on the mechanical behavior of an exponentially graded piezoelectric rotating annular plate with variable thickness, Mechanics Based Design of Structures and Machines, 50(4), 2022, 1354–1370.

[7] Allam, M.N.M, Zenkour, A.M., Tantawy, R., Analysis of functionally graded piezoelectric cylinders in a hygrothermal environment, Advances in Applied Mathematics and Mechanics, 6(2), 2014, 233-246.

[8] Allam, M.N.M., Tantawy, R., Zenkour, A.M., Magneto-thermo-elastic response of exponentially graded piezoelectric hollow spheres, Advances in Computational Design, 3(3), 2018, 303-318.

[9] Thanh, T.T., Ke, T.V., Hoa, P.Q., Van, T.T., Trung, N.T., An edge-based smoothed finite element for buckling analysis of functionally graded material variable thickness plates, Vietnam Journal of Mechanics, VAST, 43(3), 2021, 221–235.

[10] Saadatfar, M., Zarandi, M.H., Effect of angular acceleration on the mechanical behavior of an exponentially graded piezoelectric rotating annular plate with variable thickness, Mechanics Based Design of Structures and Machines, 50(4), 2022, 1354-1370.

[11] Sharma, D., Kaur, R., Sharma, H., Investigation of thermo-elastic characteristics in functionally graded rotating disk using finite element method, Nonlinear Engineering, 10(1), 2021, DOI: 10.1515/nleng-2021-0025.

[12] Chen, D., Yang, J., Kitipornchai, S., Elastic buckling and static bending of shear deformable functionally graded porous beam, Composite Structures, 133, 2015, 54–61.

[13] Kitipornchai, S., Chen, D., Yang, J., Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Materials and Design, 116, 2017, 656–665.

[14] Wang, Y., Zhang, L., Daynes, S., Zhang, H., Feih, S., Wang, M.Y., Design of graded lattice structure with optimized mesostructures for additive manufacturing, Materials and Design, 142, 2018, 114–123.

[15] Nazir, A., Jeng, J.Y., Buckling behavior of additively manufactured cellular columns: experimental and simulation validation, Materials and Design, 186, 2020, 108349.

[16] Tantawy, R., Zenkour, A.M., Effect of Porosity and Hygrothermal Environment on FGP Hollow Spheres under Electromechanical Loads, Journal of Applied and Computational Mechanics, 8(2), 2022, 710–722.

[17] Wattanasakulpong, N., Ungbhakorn, V., Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32(1), 2014, 111–120.

[18] Tantawy, R., Magneto-electric influence on a functionally graded porous hollow structure in hygrothermal environment, Scientific Journal for Damietta Faculty of Science, 12 (1), 2022, 1-15.

[19] Babaei, M., Kiarasi, F., Asemi, K., Hosseini, M., Functionally graded saturated porous structures: A review, Journal of Computational Applied Mechanics, 53(2), 2022, 297-308.

[20] Nathi, V. K., Buckling analysis of 2D functionally graded porous beams using novel higher order theory, Journal of Computational Applied Mechanics, 53(3), 2022, 393-413.

[21] Tantawy, R. M., Zenkour, A. M., Bending Response of a Rotating Viscoelastic Functionally Graded Porous Disk with Variable Thickness, Journal of Computational Applied Mechanics, 54(4), 2023, 482-500.

[22] Li, X., Wang, T., Liu, F., Zhu, Z., Computer simulation of the nonlinear static behavior of axially functionally graded microtube with porosity, Advances in Nano Research, 11(4), 2021, 437–451.

[23] Li, C., Shen, H. S., Yang, J., Nonlinear Vibration Behavior of FG Sandwich Beams with Auxetic Porous Copper Core in Thermal Environments, International Journal of Structural Stability and Dynamics, 2023, 2350144.

[24] Tantawy, R.M., Zenkour, A.M., Effects of porosity, rotation, thermomagnetic, and thickness variation on functionally graded tapered annular disks, Information Sciences Letters, 12(3), 2023, 1133–1150.

[25] Ebrahimi, F., Jafari, A., Barati, M.R., Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations, Thin-Walled Structures, 119, 2017, 33–46.

[26] Akbas, S., Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity, International Journal of Applied Mechanics, 9(5), 2017, 1750076.

[27] Tantawy, R., Zenkour, A.M., Even and uneven porosities on rotating functionally graded variable thickness annular disks with magneto-electro thermo-mechanical loadings, Journal of Applied and Computational Mechanics, 9(3), 2023, 695–711.

[28] Barati, M.R., Shahverdi, H., Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions, Journal of Fluids and Structures, 73, 2017, 125–136.

[29] Ootao, Y., Tanigawa, Y., Transient piezothermoelastic analysis for a functionally graded thermopiezoelectric hollow sphere, Composite Structures, 81, 2007, 540–549.

[30] Arani, A.G., Kolahchi, R., Mosallaie Barzoki, A.A., Loghman, A., Electro-thermo-mechanical behaviors of FGPM spheres using analytical method and ANSYS software, Applied Mathematical Modelling, 36, 2012, 139–157.

[31] Vaka, V., Sathujoda, P., Bhalla, N.A., Kumar, Y.V.S., Steady-state and transient vibration analysis of a thermally loaded power law-based functionally graded rotor system with induced porosities, Forces in Mechanics, 9, 2022, 100123.

[32] Nikarad, S.F., Kanellopoulos, A., Bodaghi, M., Chen, Z.T., Large deformation behavior of functionally graded porous curved beams in thermal environment, Archive of Applied Mechanics, 91, 2021, 2255–2278.

[33] Bayat, M., Rahimi, M., Saleem, M., Mohazzab, A. H., Wudtke, I., Talebi, H., One dimensional analysis for magnetothermo- mechanical response in a functionally graded annular variable-thickness rotating disk, Applied Mathematical Modelling, 38(19), 2014, 4625–4639.

[34] Marin, M., Öchsner, A., Bhatti, M.M., Some results in Moore‐Gibson‐Thompson thermoelasticity of dipolar bodies, ZAMM‐Journal of Applied Mathematics and Mechanics, 100(12), 2020, 1-13.

[35] Kraus, J.D., Electromagnetic, McGraw Hill. Inc., U.S.A., 1984.

[36] Dai, T., Dai, H.L., Analysis of a rotating FGMEE circular disk with variable thickness under thermal environment, Applied Mathematical Modelling, 45, 2017, 900–924.

[37] Dai, H.L., Jiang, H.J., Analytical study for electromagnetothermoelastic behavior of a functionally graded piezoelectric solid cylinder, Mechanics of Advanced Materials and Structures, 20(10), 2013, 800–811.

[38] Marin, M., Agarwal, R.P., Mahmoud, S.R., Modeling a microstretch thermo-elastic body with two temperatures, Abstract and Applied Analysis, 2013, 2013, 1-7.

[39] Vlase, S., Nastac, C., Marin, M., Mihalcica, M., A method for the study of the vibration of mechanical bars systems with symmetries, ACTA Technica Napocensis - Series: Applied Mathematics, Mechanics, And Engineering, 60(4), 2017, 539-544.

[40] Mendelson, A., Plasticity Theory and Applications, Macmillan, New York, 1968.