On Numerical Bending Analysis of Functionally Graded Porous Beam – Effect of Porosity Adapting Higher Order Shear Deformation Theory
Document Type : Research Paper
Authors
1 Department of Mechanical Engineering, MLR Institute of Technology, Hyderabad, India.
2 Department of Mathematics, Dayananda Sagar College of Engineering, Bengaluru, India.
Abstract
Pores have a significant impact on the properties of functionally graded materials. Many other features can be added if the distribution of pores are allowed to progressively increase from the surface into the inside. The bending response on a Functionally graded porous beam (FGPB) is analysed by adopting a unique shear shape function and taking into consideration even and uneven porosity distributions. Material properties of FGPBs with even and uneven porosity distributions along the length and thickness directions are changed using power law. When formulating equilibrium equations for FGPB, principle of virtual displacements is put to use. The method developed by Navier is applied in order to provide solutions to porous FGPB for simply supported boundary conditions and applied to clamped-clamped and clamped-free boundary conditions. Proposed methodology is justified with numerical findings of non-porous and porous FGPBs that are from earlier research. Exponents, porosity, volume fraction, thickness ratios, and aspect ratios are factors that have an influence on the dimensionless deflections and stresses that are being researched.
Keywords
[1] Y. Miyamoto, W. Kaysser, B. Rabin, A. Kawasaki, R. G. Ford, Processing and fabrication, Functionally Graded Materials: Design, Processing and Applications, pp. 161-245, 1999.
[2] M. Mohammadi, A. Farajpour, A. Moradi, M. Hosseini, Vibration analysis of the rotating multilayer piezoelectric Timoshenko nanobeam, Engineering Analysis with Boundary Elements, Vol. 145, pp. 117-131, 2022.
[3] M. Mohammadi, A. Rastgoo, Primary and secondary resonance analysis of FG/lipid nanoplate with considering porosity distribution based on a nonlinear elastic medium, Mechanics of Advanced Materials and Structures, Vol. 27, No. 20, pp. 1709-1730, 2020.
[4] M. Mohammadi, M. Hosseini, M. Shishesaz, A. Hadi, A. Rastgoo, Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads, European Journal of Mechanics-A/Solids, Vol. 77, pp. 103793, 2019.
[5] M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, An Int'l Journal, Vol. 69, No. 2, pp. 131-143, 2019.
[6] A. Farajpour, A. Rastgoo, M. Mohammadi, Vibration, buckling and smart control of microtubules using piezoelectric nanoshells under electric voltage in thermal environment, Physica B: Condensed Matter, Vol. 509, pp. 100-114, 2017.
[7] A. Farajpour, M. H. Yazdi, A. Rastgoo, M. Loghmani, M. Mohammadi, Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates, Composite Structures, Vol. 140, pp. 323-336, 2016.
[8] A. Farajpour, M. H. Yazdi, A. Rastgoo, M. Mohammadi, A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment, Acta Mechanica, Vol. 227, pp. 1849-1867, 2016.
[9] M. Mohammadi, M. Safarabadi, A. Rastgoo, A. Farajpour, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, Vol. 227, pp. 2207-2232, 2016.
[10] M. R. Farajpour, A. Rastgoo, A. Farajpour, M. Mohammadi, Vibration of piezoelectric nanofilm-based electromechanical sensors via higher-order non-local strain gradient theory, Micro & Nano Letters, Vol. 11, No. 6, pp. 302-307, 2016.
[11] M. Baghani, M. Mohammadi, A. Farajpour, Dynamic and stability analysis of the rotating nanobeam in a nonuniform magnetic field considering the surface energy, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650048, 2016.
[12] M. Goodarzi, M. Mohammadi, M. Khooran, F. Saadi, Thermo-mechanical vibration analysis of FG circular and annular nanoplate based on the visco-pasternak foundation, Journal of Solid Mechanics, Vol. 8, No. 4, pp. 788-805, 2016.
[13] H. Asemi, S. Asemi, A. Farajpour, M. Mohammadi, Nanoscale mass detection based on vibrating piezoelectric ultrathin films under thermo-electro-mechanical loads, Physica E: Low-dimensional Systems and Nanostructures, Vol. 68, pp. 112-122, 2015.
[14] M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, 2015.
[15] M. Goodarzi, M. Mohammadi, A. Gharib, Techno-Economic Analysis of Solar Energy for Cathodic Protection of Oil and Gas Buried Pipelines in Southwestern of Iran, in Proceeding of, https://publications.waset.org/abstracts/33008/techno-economic-analysis-of …, pp.
[16] M. Mohammadi, A. A. Nekounam, M. Amiri, The vibration analysis of the composite natural gas pipelines in the nonlinear thermal and humidity environment, in Proceeding of, https://civilica.com/doc/540946/, pp.
[17] M. Goodarzi, M. Mohammadi, M. Rezaee, Technical Feasibility Analysis of PV Water Pumping System in Khuzestan Province-Iran, in Proceeding of, https://publications.waset.org/abstracts/18930/technical-feasibility …, pp.
[18] M. Mohammadi, A. Farajpour, A. Moradi, M. Ghayour, Shear buckling of orthotropic rectangular graphene sheet embedded in an elastic medium in thermal environment, Composites Part B: Engineering, Vol. 56, pp. 629-637, 2014.
[19] M. Mohammadi, A. Moradi, M. Ghayour, A. Farajpour, Exact solution for thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 437-458, 2014.
[20] M. Mohammadi, A. Farajpour, M. Goodarzi, F. Dinari, Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium, Latin American Journal of Solids and Structures, Vol. 11, pp. 659-682, 2014.
[21] M. Mohammadi, A. Farajpour, M. Goodarzi, Numerical study of the effect of shear in-plane load on the vibration analysis of graphene sheet embedded in an elastic medium, Computational Materials Science, Vol. 82, pp. 510-520, 2014.
[22] A. Farajpour, A. Rastgoo, M. Mohammadi, Surface effects on the mechanical characteristics of microtubule networks in living cells, Mechanics Research Communications, Vol. 57, pp. 18-26, 2014.
[23] S. R. Asemi, M. Mohammadi, A. Farajpour, A study on the nonlinear stability of orthotropic single-layered graphene sheet based on nonlocal elasticity theory, Latin American Journal of Solids and Structures, Vol. 11, pp. 1541-1546, 2014.
[24] M. Goodarzi, M. Mohammadi, A. Farajpour, M. Khooran, Investigation of the effect of pre-stressed on vibration frequency of rectangular nanoplate based on a visco-Pasternak foundation, 2014.
[25] S. Asemi, A. Farajpour, H. Asemi, M. Mohammadi, Influence of initial stress on the vibration of double-piezoelectric-nanoplate systems with various boundary conditions using DQM, Physica E: Low-dimensional Systems and Nanostructures, Vol. 63, pp. 169-179, 2014.
[26] S. Asemi, A. Farajpour, M. Mohammadi, Nonlinear vibration analysis of piezoelectric nanoelectromechanical resonators based on nonlocal elasticity theory, Composite Structures, Vol. 116, pp. 703-712, 2014.
[27] M. Mohammadi, M. Ghayour, A. Farajpour, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, Vol. 45, No. 1, pp. 32-42, 2013.
[28] M. Mohammadi, M. Goodarzi, M. Ghayour, A. Farajpour, Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory, Composites Part B: Engineering, Vol. 51, pp. 121-129, 2013.
[29] M. Mohammadi, A. Farajpour, M. Goodarzi, R. Heydarshenas, Levy type solution for nonlocal thermo-mechanical vibration of orthotropic mono-layer graphene sheet embedded in an elastic medium, Journal of Solid Mechanics, Vol. 5, No. 2, pp. 116-132, 2013.
[30] M. Mohammadi, A. Farajpour, M. Goodarzi, H. Mohammadi, Temperature Effect on Vibration Analysis of Annular Graphene Sheet Embedded on Visco-Pasternak Foundati, Journal of Solid Mechanics, Vol. 5, No. 3, pp. 305-323, 2013.
[31] M. Danesh, A. Farajpour, M. Mohammadi, Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method, Mechanics Research Communications, Vol. 39, No. 1, pp. 23-27, 2012.
[32] A. Farajpour, A. Shahidi, M. Mohammadi, M. Mahzoon, Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics, Composite Structures, Vol. 94, No. 5, pp. 1605-1615, 2012.
[33] M. Mohammadi, M. Goodarzi, M. Ghayour, S. Alivand, Small scale effect on the vibration of orthotropic plates embedded in an elastic medium and under biaxial in-plane pre-load via nonlocal elasticity theory, 2012.
[34] A. Farajpour, M. Mohammadi, A. Shahidi, M. Mahzoon, Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 10, pp. 1820-1825, 2011.
[35] A. Farajpour, M. Danesh, M. Mohammadi, Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 3, pp. 719-727, 2011.
[36] H. Moosavi, M. Mohammadi, A. Farajpour, S. Shahidi, Vibration analysis of nanorings using nonlocal continuum mechanics and shear deformable ring theory, Physica E: Low-dimensional Systems and Nanostructures, Vol. 44, No. 1, pp. 135-140, 2011.
[37] M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version differential quadrature method, Journal of solid mechanics in engineering, Vol. 3, No. 2, pp. 47-56, 2011.
[38] A. Farajpour, M. Mohammadi, M. Ghayour, Shear buckling of rectangular nanoplates embedded in elastic medium based on nonlocal elasticity theory, in Proceeding of, www.civilica.com/Paper-ISME19-ISME19_390.html, pp. 390.
[39] M. Mohammadi, A. Farajpour, A. R. Shahidi, Higher order shear deformation theory for the buckling of orthotropic rectangular nanoplates using nonlocal elasticity, in Proceeding of, www.civilica.com/Paper-ISME19-ISME19_391.html, pp. 391.
[40] M. Mohammadi, A. Farajpour, A. R. Shahidi, Effects of boundary conditions on the buckling of single-layered graphene sheets based on nonlocal elasticity, in Proceeding of, www.civilica.com/Paper-ISME19-ISME19_382.html, pp. 382.
[41] M. Mohammadi, M. Ghayour, A. Farajpour, Using of new version integral differential method to analysis of free vibration orthotropic sector plate based on elastic medium, in Proceeding of, www.civilica.com/Paper-ISME19-ISME19_497.html, pp. 497.
[42] M. Mohammadi, A. Farajpour, A. Rastgoo, Coriolis effects on the thermo-mechanical vibration analysis of the rotating multilayer piezoelectric nanobeam, Acta Mechanica, Vol. 234, No. 2, pp. 751-774, 2023/02/01, 2023.
[43] J. Kim, K. K. Żur, J. Reddy, Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates, Composite Structures, Vol. 209, pp. 879-888, 2019.
[44] J. Parthasarathy, B. Starly, S. Raman, A design for the additive manufacture of functionally graded porous structures with tailored mechanical properties for biomedical applications, Journal of Manufacturing Processes, Vol. 13, No. 2, pp. 160-170, 2011.
[45] M. Babaei, F. Kiarasi, K. Asemi, M. Hosseini, Functionally graded saturated porous structures: A review, Journal of Computational Applied Mechanics, Vol. 53, No. 2, pp. 297-308, 2022.
[46] N.-D. Nguyen, T.-N. Nguyen, T.-K. Nguyen, T. P. Vo, A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams, Composite Structures, Vol. 282, pp. 115095, 2022.
[47] N. Wattanasakulpong, B. G. Prusty, D. W. Kelly, Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams, International Journal of Mechanical Sciences, Vol. 53, No. 9, pp. 734-743, 2011.
[48] A. Melaibari, R. M. Abo-bakr, S. Mohamed, M. Eltaher, Static stability of higher order functionally graded beam under variable axial load, Alexandria Engineering Journal, Vol. 59, No. 3, pp. 1661-1675, 2020.
[49] D. Chen, S. Kitipornchai, J. Yang, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Structures, Vol. 107, pp. 39-48, 2016.
[50] D. Chen, J. Yang, S. Kitipornchai, Free and forced vibrations of shear deformable functionally graded porous beams, International journal of mechanical sciences, Vol. 108, pp. 14-22, 2016.
[51] D. Wu, A. Liu, Y. Huang, Y. Huang, Y. Pi, W. Gao, Dynamic analysis of functionally graded porous structures through finite element analysis, Engineering Structures, Vol. 165, pp. 287-301, 2018.
[52] K. Gao, R. Li, J. Yang, Dynamic characteristics of functionally graded porous beams with interval material properties, Engineering Structures, Vol. 197, pp. 109441, 2019.
[53] A. R. Noori, T. A. Aslan, B. Temel, Dynamic analysis of functionally graded porous beams using complementary functions method in the Laplace domain, Composite Structures, Vol. 256, pp. 113094, 2021.
[54] Z. Lei, L. Zhang, K. Liew, J. Yu, Dynamic stability analysis of carbon nanotube-reinforced functionally graded cylindrical panels using the element-free kp-Ritz method, Composite Structures, Vol. 113, pp. 328-338, 2014.
[55] M. Filippi, M. Petrolo, S. Valvano, E. Carrera, Analysis of laminated composites and sandwich structures by trigonometric, exponential and miscellaneous polynomials and a MITC9 plate element, Composite Structures, Vol. 150, pp. 103-114, 2016.
[56] F. A. Fazzolari, Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations, Composites Part B: Engineering, Vol. 136, pp. 254-271, 2018.
[57] O. Polit, C. Anant, B. Anirudh, M. Ganapathi, Functionally graded graphene reinforced porous nanocomposite curved beams: Bending and elastic stability using a higher-order model with thickness stretch effect, Composites Part B: Engineering, Vol. 166, pp. 310-327, 2019.
[58] R. Shimpi, P. Guruprasad, K. Pakhare, Simple two variable refined theory for shear deformable isotropic rectangular beams, Journal of Applied and Computational Mechanics, Vol. 6, No. 3, pp. 394-415, 2020.
[59] A. Assie, S. D. Akbas, A. M. Kabeel, A. A. Abdelrahman, M. A. Eltaher, Dynamic analysis of porous functionally graded layered deep beams with viscoelastic core, STEEL AND COMPOSITE STRUCTURES, Vol. 43, No. 1, pp. 79-90, 2022.
[60] B. Anirudh, M. Ganapathi, C. Anant, O. Polit, A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling, Composite Structures, Vol. 222, pp. 110899, 2019.
[61] W. Fang, T. Yu, T. Q. Bui, Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis, Composite Structures, Vol. 221, pp. 110890, 2019.
[62] F. Ebrahimi, N. Farazmandnia, Vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in thermal environment, Advances in aircraft and spacecraft science, Vol. 5, No. 1, pp. 107, 2018.
[63] Y. S. Al Rjoub, A. G. Hamad, Free Vibration of Axially Loaded Multi-Cracked Beams Using the Transfer Matrix Method, International Journal of Acoustics & Vibration, Vol. 24, No. 1, 2019.
[64] J. Zhao, Q. Wang, X. Deng, K. Choe, R. Zhong, C. Shuai, Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions, Composites Part B: Engineering, Vol. 168, pp. 106-120, 2019.
[65] M. Jamshidi, J. Arghavani, Optimal material tailoring of functionally graded porous beams for buckling and free vibration behaviors, Mechanics Research Communications, Vol. 88, pp. 19-24, 2018.
[66] V. K. Nathi, Buckling analysis of 2D functionally graded porous beams using novel higher order theory, Journal of Computational Applied Mechanics, Vol. 53, No. 3, pp. 393-413, 2022.
[67] A. Karamanlı, Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory, Composite Structures, Vol. 189, pp. 127-136, 2018.
[68] T. P. Vo, H.-T. Thai, T.-K. Nguyen, F. Inam, J. Lee, Static behaviour of functionally graded sandwich beams using a quasi-3D theory, Composites Part B: Engineering, Vol. 68, pp. 59-74, 2015.
[69] A. Karamanlı, Bending analysis of two directional functionally graded beams using a four-unknown shear and normal deformation theory, Politeknik Dergisi, Vol. 21, No. 4, pp. 861-874, 2018.
[70] G. Reddy, N. V. Kumar, Bending Analysis of 2-D Functionally Graded Porous Beams Based on Novel High Order Theory, Journal of Engineering Science & Technology Review, Vol. 15, No. 5, 2022.
)
Volume 54, Issue 1
March 2023Pages 49-67
- Receive Date: 02 January 2023
- Revise Date: 29 January 2023
- Accept Date: 29 January 2023