A refined inverse hyperbolic shear deformation theory for bending analysis of functionally graded porous plates
Document Type : Research Paper
Authors
1 Department of Mechanical Engineering, Rajeev Gandhi Memorial College of Engineering and Technology, Nandyal
2 Department of Mechanical Engineering, Jawaharlal Nehru Technological University, Hyderabad
Abstract
The modern engineering structures require the advanced engineering materials to resist the high temperatures and to provide high stiffness. In particular the functionally graded porous materials (FGPMs) introduced are expected to have these desired properties, consequently eliminating local stress concentration and de-lamination. In the present paper, a new shear strains shape function is chosen to research the bending analysis of functionally graded plates (FGPs) with uneven symmetrical, uneven asymmetrical and even distributions of porosity. The material properties of uneven porosity distributions along the thickness of the FGPs vary with cosine function. The present theory includes the influence of thickness stretching. This theory also fulfills the nullity of the shear stresses in the transverse direction on the top and bottom of the plate, thus avoids the use of a shear correction factor. The virtual displacement principle is employed to develop the equilibrium equations for porous FGPs. The Navier’s method is used to obtain the solutions of porous FGPs for simply supported (SS) conditions. The accuracy of the developed theory is established with numerical results of perfect and porous FGPs available in the open source. The transverse displacements and stress results have been reported and studied for evenly, unevenly symmetrical and unevenly asymmetrical distributions with different porosity volume fraction (PVF), thickness ratios and aspect ratios. From the numerical results it is concluded that the type of porosity distribution needs to be considered as a key factor in the optimal design of the porous FGPs.
Keywords
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[13] Z. Mazarei, M. Z. Nejad, A. Hadi, Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650054, 2016.
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[15] M. Zamani Nejad, M. Jabbari, A. Hadi, A review of functionally graded thick cylindrical and conical shells, Journal of Computational Applied Mechanics, Vol. 48, No. 2, pp. 357-370, 2017.
[16] A. Hadi, A. Rastgoo, N. Haghighipour, A. Bolhassani, Numerical modelling of a spheroid living cell membrane under hydrostatic pressure, Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, No. 8, pp. 083501, 2018.
[17] M. Z. Nejad, N. Alamzadeh, A. Hadi, Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition, Composites Part B: Engineering, Vol. 154, pp. 410-422, 2018.
[18] B. Karami, D. Shahsavari, M. Janghorban, L. Li, On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory, International Journal of Engineering Science, Vol. 144, pp. 103143, 2019.
[19] E. Zarezadeh, V. Hosseini, A. Hadi, Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory, Mechanics Based Design of Structures and Machines, Vol. 48, No. 4, pp. 480-495, 2020.
[20] 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.
[21] 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.
[22] 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.
[23] N. GHAYOUR, A. Sedaghat, M. Mohammadi, Wave propagation approach to fluid filled submerged visco-elastic finite cylindrical shells, 2011.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[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, 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, No. 4, pp. 659-682, 2014.
[31] 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, No. 3, pp. 437-458, 2014.
[32] 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.
[33] 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.
[34] 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.
[35] 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.
[36] 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, No. 9, pp. 1515-1540, 2014.
[37] 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.
[38] 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.
[39] 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.
[40] 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.
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[42] 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, No. 7, pp. 1849-1867, 2016.
[43] 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.
[44] 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, No. 8, pp. 2207-2232, 2016.
[45] 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, pp. 1-22, 2018.
[46] M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, Vol. 69, No. 2, pp. 131, 2019.
[47] 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.
[48] B. S. Reddy, J. S. Kumar, C. E. Reddy, K. Reddy, Buckling analysis of functionally graded material plates using higher order shear deformation theory, Journal of composites, Vol. 2013, 2013.
[49] B. S. Redddy, J. S. Kumar, C. E. Reddy, K. V. K. Reddy, Free vibration behaviour of functionally graded plates using higher-order shear deformation theory, Journal of Applied Science and Engineering, Vol. 17, No. 3, pp. 231-241, 2014.
[50] B. SiddaRedddy, J. S. Kumar, C. EswaraReddy, K. Reddy, Static Bending Behavior of Functionally Graded Plates Subjected to Mechanical Loading, Jordan Journal of Mechanical & Industrial Engineering, Vol. 8, No. 4, 2014.
[51] B. S. Reddy, J. S. Kumar, C. Reddy, K. V. K. Reddy, Buckling analysis of functionally graded plates using higher order shear deformation theory with thickness stretching effect, International Journal of Applied Science and Engineering, Vol. 13, No. 1, pp. 19-36, 2015.
[52] S. R. Bathini, Thermomechanical behaviour of Functionally Graded Plates with HSDT, Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 2019.
[53] B. S. Reddy, Bending Behaviour Of Exponentially Graded Material Plates Using New Higher Order Shear Deformation Theory with Stretching Effect, International Journal of Engineering Research, Vol. 3, pp. 124-131, 2014.
[54] B. S. Reddy, A. R. Reddy, J. S. Kumar, K. V. K. Reddy, Bending analysis of laminated composite plates using finite element method, International journal of engineering, science and technology, Vol. 4, No. 2, pp. 177-190, 2012.
[55] J. S. Kumar, B. S. Reddy, C. E. Reddy, K. V. K. Reddy, Geometrically non linear analysis of functionally graded material plates using higher order theory, International Journal of Engineering, Science and Technology, Vol. 3, No. 1, 2011.
[56] K. Suresh, S. R. Jyothula, E. R. Bathini, K. Vijaya, Nonlinear thermal analysis of functionally graded plates using higher order theory, Innovative Systems Design and Engineering, Vol. 2, No. 5, pp. 1-13, 2011.
[57] A. M. Zenkour, A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities, Composite Structures, Vol. 201, pp. 38-48, 2018.
[58] S. Merdaci, H. Belghoul, High-order shear theory for static analysis of functionally graded plates with porosities, Comptes Rendus Mécanique, Vol. 347, No. 3, pp. 207-217, 2019.
[59] 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.
[60] Ş. D. Akbaş, Vibration and static analysis of functionally graded porous plates, Journal of Applied and Computational Mechanics, Vol. 3, No. 3, pp. 199-207, 2017.
[61] N. V. Nguyen, H. X. Nguyen, S. Lee, H. Nguyen-Xuan, Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates, Advances in Engineering Software, Vol. 126, pp. 110-126, 2018.
[62] K. Li, D. Wu, X. Chen, J. Cheng, Z. Liu, W. Gao, M. Liu, Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets, Composite Structures, Vol. 204, pp. 114-130, 2018.
[63] M. Slimane, Analysis of Bending of Ceramic-Metal Functionally Graded Plates with Porosities Using of High Order Shear Theory, in Proceeding of.
[64] P. A. Demirhan, V. Taskin, Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach, Composites Part B: Engineering, Vol. 160, pp. 661-676, 2019.
[65] S. Coskun, J. Kim, H. Toutanji, Bending, free vibration, and buckling analysis of functionally graded porous micro-plates using a general third-order plate theory, Journal of Composites Science, Vol. 3, No. 1, pp. 15, 2019.
[66] 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.
[67] D. Chen, J. Yang, S. Kitipornchai, Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method, Archives of Civil and Mechanical Engineering, Vol. 19, No. 1, pp. 157-170, 2019.
[68] A. A. Daikh, A. M. Zenkour, Effect of porosity on the bending analysis of various functionally graded sandwich plates, Materials Research Express, Vol. 6, No. 6, pp. 065703, 2019.
[69] A. Farzam, B. Hassani, Isogeometric analysis of in-plane functionally graded porous microplates using modified couple stress theory, Aerospace Science and Technology, Vol. 91, pp. 508-524, 2019.
[70] S. Bathini, K. Vijaya Kumar Reddy, Flexural behavior of porous functionally graded plates using a novel higher order theory, Journal of Computational Applied Mechanics, 2020.
[71] A. Zenkour, Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate, Archive of Applied Mechanics, Vol. 77, No. 4, pp. 197-214, 2007.
[72] J. Mantari, C. G. Soares, A novel higher-order shear deformation theory with stretching effect for functionally graded plates, Composites Part B: Engineering, Vol. 45, No. 1, pp. 268-281, 2013.
[73] J. Mantari, C. G. Soares, Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory, Composite Structures, Vol. 94, No. 6, pp. 1991-2000, 2012.
[1] 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.
[2] N. Wattanasakulpong, A. Chaikittiratana, S. Pornpeerakeat, Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory, Acta Mechanica Sinica, Vol. 34, No. 6, pp. 1124-1135, 2018.
[3] M. Mohammadi, M. Ghayour, A. Farajpour, Analysis of free vibration sector plate based on elastic medium by using new version of differential quadrature method, Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, Vol. 3, No. 2, pp. 47-56, 2010.
[4] 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.
[5] M. Safarabadi, M. Mohammadi, A. Farajpour, M. Goodarzi, Effect of surface energy on the vibration analysis of rotating nanobeam, 2015.
[6] 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.
[7] 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.
[8] M. Zamani Nejad, A. Rastgoo, A. Hadi, Effect of exponentially-varying properties on displacements and stresses in pressurized functionally graded thick spherical shells with using iterative technique, Journal of Solid Mechanics, Vol. 6, No. 4, pp. 366-377, 2014.
[9] M. Z. Nejad, A. Rastgoo, A. Hadi, Exact elasto-plastic analysis of rotating disks made of functionally graded materials, International Journal of Engineering Science, Vol. 85, pp. 47-57, 2014.
[10] M. Hosseini, M. Shishesaz, K. N. Tahan, A. Hadi, Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials, International Journal of Engineering Science, Vol. 109, pp. 29-53, 2016.
[11] M. Shishesaz, M. Hosseini, K. N. Tahan, A. Hadi, Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory, Acta Mechanica, Vol. 228, No. 12, pp. 4141-4168, 2017.
[12] M. Hosseini, M. Shishesaz, A. Hadi, Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness, Thin-Walled Structures, Vol. 134, pp. 508-523, 2019.
[13] Z. Mazarei, M. Z. Nejad, A. Hadi, Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials, International Journal of Applied Mechanics, Vol. 8, No. 04, pp. 1650054, 2016.
[14] M. Gharibi, M. Zamani Nejad, A. Hadi, Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius, Journal of Computational Applied Mechanics, Vol. 48, No. 1, pp. 89-98, 2017.
[15] M. Zamani Nejad, M. Jabbari, A. Hadi, A review of functionally graded thick cylindrical and conical shells, Journal of Computational Applied Mechanics, Vol. 48, No. 2, pp. 357-370, 2017.
[16] A. Hadi, A. Rastgoo, N. Haghighipour, A. Bolhassani, Numerical modelling of a spheroid living cell membrane under hydrostatic pressure, Journal of Statistical Mechanics: Theory and Experiment, Vol. 2018, No. 8, pp. 083501, 2018.
[17] M. Z. Nejad, N. Alamzadeh, A. Hadi, Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition, Composites Part B: Engineering, Vol. 154, pp. 410-422, 2018.
[18] B. Karami, D. Shahsavari, M. Janghorban, L. Li, On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory, International Journal of Engineering Science, Vol. 144, pp. 103143, 2019.
[19] E. Zarezadeh, V. Hosseini, A. Hadi, Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory, Mechanics Based Design of Structures and Machines, Vol. 48, No. 4, pp. 480-495, 2020.
[20] 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.
[21] 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.
[22] 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.
[23] N. GHAYOUR, A. Sedaghat, M. Mohammadi, Wave propagation approach to fluid filled submerged visco-elastic finite cylindrical shells, 2011.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[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, 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, No. 4, pp. 659-682, 2014.
[31] 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, No. 3, pp. 437-458, 2014.
[32] 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.
[33] 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.
[34] 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.
[35] 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.
[36] 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, No. 9, pp. 1515-1540, 2014.
[37] 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.
[38] 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.
[39] 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.
[40] 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.
[41] 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.
[42] 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, No. 7, pp. 1849-1867, 2016.
[43] 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.
[44] 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, No. 8, pp. 2207-2232, 2016.
[45] 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, pp. 1-22, 2018.
[46] M. Mohammadi, A. Rastgoo, Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core, Structural Engineering and Mechanics, Vol. 69, No. 2, pp. 131, 2019.
[47] 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.
[48] B. S. Reddy, J. S. Kumar, C. E. Reddy, K. Reddy, Buckling analysis of functionally graded material plates using higher order shear deformation theory, Journal of composites, Vol. 2013, 2013.
[49] B. S. Redddy, J. S. Kumar, C. E. Reddy, K. V. K. Reddy, Free vibration behaviour of functionally graded plates using higher-order shear deformation theory, Journal of Applied Science and Engineering, Vol. 17, No. 3, pp. 231-241, 2014.
[50] B. SiddaRedddy, J. S. Kumar, C. EswaraReddy, K. Reddy, Static Bending Behavior of Functionally Graded Plates Subjected to Mechanical Loading, Jordan Journal of Mechanical & Industrial Engineering, Vol. 8, No. 4, 2014.
[51] B. S. Reddy, J. S. Kumar, C. Reddy, K. V. K. Reddy, Buckling analysis of functionally graded plates using higher order shear deformation theory with thickness stretching effect, International Journal of Applied Science and Engineering, Vol. 13, No. 1, pp. 19-36, 2015.
[52] S. R. Bathini, Thermomechanical behaviour of Functionally Graded Plates with HSDT, Journal of Computational & Applied Research in Mechanical Engineering (JCARME), 2019.
[53] B. S. Reddy, Bending Behaviour Of Exponentially Graded Material Plates Using New Higher Order Shear Deformation Theory with Stretching Effect, International Journal of Engineering Research, Vol. 3, pp. 124-131, 2014.
[54] B. S. Reddy, A. R. Reddy, J. S. Kumar, K. V. K. Reddy, Bending analysis of laminated composite plates using finite element method, International journal of engineering, science and technology, Vol. 4, No. 2, pp. 177-190, 2012.
[55] J. S. Kumar, B. S. Reddy, C. E. Reddy, K. V. K. Reddy, Geometrically non linear analysis of functionally graded material plates using higher order theory, International Journal of Engineering, Science and Technology, Vol. 3, No. 1, 2011.
[56] K. Suresh, S. R. Jyothula, E. R. Bathini, K. Vijaya, Nonlinear thermal analysis of functionally graded plates using higher order theory, Innovative Systems Design and Engineering, Vol. 2, No. 5, pp. 1-13, 2011.
[57] A. M. Zenkour, A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities, Composite Structures, Vol. 201, pp. 38-48, 2018.
[58] S. Merdaci, H. Belghoul, High-order shear theory for static analysis of functionally graded plates with porosities, Comptes Rendus Mécanique, Vol. 347, No. 3, pp. 207-217, 2019.
[59] 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.
[60] Ş. D. Akbaş, Vibration and static analysis of functionally graded porous plates, Journal of Applied and Computational Mechanics, Vol. 3, No. 3, pp. 199-207, 2017.
[61] N. V. Nguyen, H. X. Nguyen, S. Lee, H. Nguyen-Xuan, Geometrically nonlinear polygonal finite element analysis of functionally graded porous plates, Advances in Engineering Software, Vol. 126, pp. 110-126, 2018.
[62] K. Li, D. Wu, X. Chen, J. Cheng, Z. Liu, W. Gao, M. Liu, Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets, Composite Structures, Vol. 204, pp. 114-130, 2018.
[63] M. Slimane, Analysis of Bending of Ceramic-Metal Functionally Graded Plates with Porosities Using of High Order Shear Theory, in Proceeding of.
[64] P. A. Demirhan, V. Taskin, Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach, Composites Part B: Engineering, Vol. 160, pp. 661-676, 2019.
[65] S. Coskun, J. Kim, H. Toutanji, Bending, free vibration, and buckling analysis of functionally graded porous micro-plates using a general third-order plate theory, Journal of Composites Science, Vol. 3, No. 1, pp. 15, 2019.
[66] 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.
[67] D. Chen, J. Yang, S. Kitipornchai, Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method, Archives of Civil and Mechanical Engineering, Vol. 19, No. 1, pp. 157-170, 2019.
[68] A. A. Daikh, A. M. Zenkour, Effect of porosity on the bending analysis of various functionally graded sandwich plates, Materials Research Express, Vol. 6, No. 6, pp. 065703, 2019.
[69] A. Farzam, B. Hassani, Isogeometric analysis of in-plane functionally graded porous microplates using modified couple stress theory, Aerospace Science and Technology, Vol. 91, pp. 508-524, 2019.
[70] S. Bathini, K. Vijaya Kumar Reddy, Flexural behavior of porous functionally graded plates using a novel higher order theory, Journal of Computational Applied Mechanics, 2020.
[71] A. Zenkour, Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate, Archive of Applied Mechanics, Vol. 77, No. 4, pp. 197-214, 2007.
[72] J. Mantari, C. G. Soares, A novel higher-order shear deformation theory with stretching effect for functionally graded plates, Composites Part B: Engineering, Vol. 45, No. 1, pp. 268-281, 2013.
[73] J. Mantari, C. G. Soares, Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory, Composite Structures, Vol. 94, No. 6, pp. 1991-2000, 2012.
)
Volume 51, Issue 2
December 2020Pages 417-431
- Receive Date: 18 August 2020
- Revise Date: 02 September 2020
- Accept Date: 03 September 2020