Journal of Computational Applied Mechanics

Analyzing the Buckling Behavior of In-plane Bidirectional Functionally Graded Porous Plates

Document Type : Research Paper

Authors

1 Department of Mechanical Engineering, Rajeev Gandhi Memorial College of Engineering and Technology, Nandyal-518501, A.P, India

2 Department of Mechanical Engineering, Jawaharlal Nehru Technological University, Hyderabad, India

Abstract

The spacecraft and space shuttles demand novel engineering materials to meet the required properties. This can be accomplished by altering the material properties in more than one direction. The introduction of inplane bidirectional functionally graded materials with porosity are expected to exhibit these properties. This paper presents the buckling analses of inplane bidirectional (2-D) functionally graded porous plates (IBFGPPs) considering uniform porosity distribution in uni-axial and bi-axial compression. The effective modulus of elasticity of the material is varied in in x-and y-axes by employing the rule of mixtures. The higherorder theory used for the study of buckling response meets the nullity requirements at plate’s upper and lower surface and derived the equations of motion thru Lagrange equations. The displacement functions are formulated in simple algebraic polynomials, incorporating admissible functions to satisfy the simply supported conditions in both axial and transverse directions. The components of admissible functions are derived by Pascal’s triangle. Accurateness of this theory is judged by comparing it to existing numerical data in the literature. The effect of thickness ratio’s (a/h), aspect ratio’s (b/a), exponents (ζ_1and ζ_2) in η_1 and η_2-direction, and the porosity on the buckling response of IBFGPPs are examined comprehensively. The numerical findings provided here serve as reference solutions for evaluating diverse plate theories and for comparing them against results obtained through alternative analytical and finite element techniques. From the obtained results, it can be inferred that the proposed theory facilitates the assessing of buckling tendencies of in-plane bi-directional porous FG plates produced through sintering process and could be deemed as a pivotal in the process of optimizing the design of the IBFGPPs.

Keywords

Main Subjects

[1]          M. Koizumi, FGM activities in Japan, Composites Part B: Engineering, Vol. 28, No. 1, pp. 1-4, 1997/01/01/, 1997.
[2]          D. Chen, J. Yang, S. Kitipornchai, Free and forced vibrations of shear deformable functionally graded porous beams, International Journal of Mechanical Sciences, Vol. 108-109, pp. 14-22, 2016/04/01/, 2016.
[3]          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, 2018/12/01, 2018.
[4]          S. Bathini, K. Vijaya Kumar Reddy, Flexural behaviour  of porous functionally graded plates using a novel higher order theory, Journal of Computational Applied Mechanics, Vol. 51, No. 2, pp. 361-373, 2020.
[5]          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, pp. 15, 02/01, 2019.
[6]          M. Mohammadi, A. R. Saidi, E. Jomehzadeh, Levy Solution for Buckling Analysis of Functionally Graded Rectangular Plates, Applied Composite Materials, Vol. 17, No. 2, pp. 81-93, 2010/04/01, 2010.
[7]          M. Mohammadi, A. R. Saidi, E. Jomehzadeh, A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 224, No. 9, pp. 1831-1841, 2010/09/01, 2010.
[8]          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.
[9]          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.
[10]        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.
[11]        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.
[12]        M. Abdollahi, A. R. Saidi, M. Mohammadi, Buckling analysis of thick functionally graded piezoelectric plates based on the higher-order shear and normal deformable theory, Acta Mechanica, Vol. 226, No. 8, pp. 2497-2510, 2015/08/01, 2015.
[13]        M. Mohammadi, M. Fooladi Mahani, An analytical solution for buckling analysis of size-dependent rectangular micro-plates according to the modified strain gradient and couple stress theories, Acta Mechanica, Vol. 226, No. 10, pp. 3477-3493, 2015/10/01, 2015.
[14]        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.
[15]        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.
[16]        B. S. Reddy, J. S. Kumar, C. E. Reddy, K. V. K. Reddy, Buckling Analysis of Functionally Graded Material Plates Using Higher Order Shear Deformation Theory, Journal of Composites, Vol. 2013, pp. 808764, 2013/12/23, 2013.
[17]        B. S. Reddy, J. S. Kumar, C. E. 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. 19-35, 2015/03/01, 2015.
[18]        J. Kim, K. K. Żur, J. N. Reddy, Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates, Composite Structures, Vol. 209, pp. 879-888, 2019/02/01/, 2019.
[19]        P. Van Vinh, N. Van Chinh, A. Tounsi, Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM, European Journal of Mechanics - A/Solids, Vol. 96, pp. 104743, 2022/11/01/, 2022.
[20]        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, 2019/03/01, 2019.
[21]        M. Nemat-Alla, Reduction of thermal stresses by developing two-dimensional functionally graded materials, International Journal of Solids and Structures, Vol. 40, No. 26, pp. 7339-7356, 2003/12/01/, 2003.
[22]        P. V. Vinh, Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method, Journal of Sandwich Structures & Materials, Vol. 24, No. 2, pp. 860-899, 2022/02/01, 2021.
[23]        M. Nemat-Alla, Reduction of thermal stresses by composition optimization of two-dimensional functionally graded materials, Acta Mechanica, Vol. 208, No. 3, pp. 147-161, 2009/12/01, 2009.
[24]        M. Asgari, M. Akhlaghi, Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations, European Journal of Mechanics - A/Solids, Vol. 30, No. 2, pp. 72-81, 2011/03/01/, 2011.
[25]        M. J. Ebrahimi, M. M. Najafizadeh, Free vibration analysis of two-dimensional functionally graded cylindrical shells, Applied Mathematical Modelling, Vol. 38, No. 1, pp. 308-324, 2014/01/01/, 2014.
[26]        L. Li, X. Li, Y. Hu, Nonlinear bending of a two-dimensionally functionally graded beam, Composite Structures, Vol. 184, pp. 1049-1061, 2018/01/15/, 2018.
[27]        M. Şimşek, Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions, Composite Structures, Vol. 133, pp. 968-978, 2015/12/01/, 2015.
[28]        Y. Tang, Q. Ding, Nonlinear vibration analysis of a bi-directional functionally graded beam under hygro-thermal loads, Composite Structures, Vol. 225, pp. 111076, 2019/10/01/, 2019.
[29]        M. Şimşek, Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions, Composite Structures, Vol. 149, pp. 304-314, 2016/08/01/, 2016.
[30]        M. Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory, International Journal of Engineering Science, Vol. 103, pp. 1-10, 2016/06/01/, 2016.
[31]        A. Karamanlı, Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory, Composite Structures, Vol. 174, pp. 70-86, 2017/08/15/, 2017.
[32]        M. Lezgy-Nazargah, Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach, Aerospace Science and Technology, Vol. 45, pp. 154-164, 2015/09/01/, 2015.
[33]        M. K. Apalak, M. D. Demirbas, Thermal stress analysis of in-plane two-directional functionally graded plates subjected to in-plane edge heat fluxes, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, Vol. 232, No. 8, pp. 693-716, 2018/08/01, 2016.
[34]        T. Van Do, D. K. Nguyen, N. D. Duc, D. H. Doan, T. Q. Bui, Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory, Thin-Walled Structures, Vol. 119, pp. 687-699, 2017/10/01/, 2017.
[35]        Q. X. Lieu, S. Lee, J. Kang, J. Lee, Bending and free vibration analyses of in-plane bi-directional functionally graded plates with variable thickness using isogeometric analysis, Composite Structures, Vol. 192, pp. 434-451, 2018/05/15/, 2018.
[36]        Q. X. Lieu, D. Lee, J. Kang, J. Lee, NURBS-based modeling and analysis for free vibration and buckling problems of in-plane bi-directional functionally graded plates, Mechanics of Advanced Materials and Structures, Vol. 26, No. 12, pp. 1064-1080, 2019/06/18, 2019.
[37]        M. Chen, G. Jin, X. Ma, Y. Zhang, T. Ye, Z. Liu, Vibration analysis for sector cylindrical shells with bi-directional functionally graded materials and elastically restrained edges, Composites Part B: Engineering, Vol. 153, pp. 346-363, 2018/11/15/, 2018.
[38]        M. Esmaeilzadeh, M. Kadkhodayan, Dynamic analysis of stiffened bi-directional functionally graded plates with porosities under a moving load by dynamic relaxation method with kinetic damping, Aerospace Science and Technology, Vol. 93, pp. 105333, 2019/10/01/, 2019.
[39]        A. Barati, A. Hadi, M. Z. Nejad, R. Noroozi, On vibration of bi-directional functionally graded nanobeams under magnetic field, Mechanics Based Design of Structures and Machines, Vol. 50, No. 2, pp. 468-485, 2022/02/01, 2022.
[40]        X. Chen, Y. Lu, Z. Wu, Y. Shao, X. Xue, Y. Wu, Free vibration of in-plane bi-directional functionally graded materials rectangular plates with geometric imperfections and general elastic restraints, Aerospace Science and Technology, Vol. 132, pp. 108045, 2023/01/01/, 2023.
[41]        J. Zhu, Z. Lai, Z. Yin, J. Jeon, S. Lee, Fabrication of ZrO2–NiCr functionally graded material by powder metallurgy, Materials Chemistry and Physics, Vol. 68, No. 1, pp. 130-135, 2001/02/15/, 2001.
[42]        S. R. Bathini, V. K. R. K, C. A. B, Free vibration behaviour  of bi-directional functionally graded plates with porosities using a refined first order shear deformation theory, Journal of Computational Applied Mechanics, Vol. 51, No. 2, pp. 374-388, 2020.
[43]        R. Kolahchi, M. Safari, M. Esmailpour, Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium, Composite Structures, Vol. 150, pp. 255-265, 2016.
[44]        R. Kolahchi, S.-P. Zhu, B. Keshtegar, N.-T. Trung, Dynamic buckling optimization of laminated aircraft conical shells with hybrid nanocomposite martial, Aerospace Science and Technology, Vol. 98, pp. 105656, 2020.
[45]        B. Keshtegar, A. Farrokhian, R. Kolahchi, N.-T. Trung, Dynamic stability response of truncated nanocomposite conical shell with magnetostrictive face sheets utilizing higher order theory of sandwich panels, European Journal of Mechanics-A/Solids, Vol. 82, pp. 104010, 2020.
[46]        B. Keshtegar, M. Motezaker, R. Kolahchi, N.-T. Trung, Wave propagation and vibration responses in porous smart nanocomposite sandwich beam resting on Kerr foundation considering structural damping, Thin-Walled Structures, Vol. 154, pp. 106820, 2020.
[47]        H. Golabchi, R. Kolahchi, M. R. Bidgoli, Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects, Computers and Concrete, An International Journal, Vol. 21, No. 4, pp. 431-440, 2018.
[48]        M. H. Hajmohammad, M. Maleki, R. Kolahchi, Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer, Soil Dynamics and Earthquake Engineering, Vol. 110, pp. 18-27, 2018.
[49]        M. S. H. Al-Furjan, A. Farrokhian, B. Keshtegar, R. Kolahchi, N.-T. Trung, Dynamic stability control of viscoelastic nanocomposite piezoelectric sandwich beams resting on Kerr foundation based on exponential piezoelasticity theory, European Journal of Mechanics - A/Solids, Vol. 86, pp. 104169, 2021/03/01/, 2021.
[50]        M. Al-Furjan, A. Farrokhian, S. Mahmoud, R. Kolahchi, Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact, Thin-Walled Structures, Vol. 163, pp. 107706, 2021.
[51]        M. H. Hajmohammad, A. H. Nouri, M. S. Zarei, R. Kolahchi, A new numerical approach and visco-refined zigzag theory for blast analysis of auxetic honeycomb plates integrated by multiphase nanocomposite facesheets in hygrothermal environment, Engineering with Computers, Vol. 35, pp. 1141-1157, 2019.
[52]        R. Kolahchi, F. Kolahdouzan, A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions, Applied Mathematical Modelling, Vol. 91, pp. 458-475, 2021.
[53]        M. H. Hajmohammad, M. B. Azizkhani, R. Kolahchi, Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis, International Journal of Mechanical Sciences, Vol. 137, pp. 205-213, 2018.
[54]        M. Al-Furjan, A. Farrokhian, B. Keshtegar, R. Kolahchi, N.-T. Trung, Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones, Aerospace Science and Technology, Vol. 107, pp. 106259, 2020.
[55]        H.-T. Thai, D.-H. Choi, An efficient and simple refined theory for buckling analysis of functionally graded plates, Applied Mathematical Modelling, Vol. 36, No. 3, pp. 1008-1022, 2012/03/01/, 2012.
[56]        A. M. Zenkour, Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, Vol. 30, No. 1, pp. 67-84, 2006/01/01/, 2006.
[57]        H.-T. Thai, S.-E. Kim, Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation, International Journal of Mechanical Sciences, Vol. 75, pp. 34-44, 2013/10/01/, 2013.
[58]        X. Zhao, Y. Y. Lee, K. M. Liew, Mechanical and thermal buckling analysis of functionally graded plates, Composite Structures, Vol. 90, No. 2, pp. 161-171, 2009/09/01/, 2009.
Journal of Computational Applied Mechanics
Volume 55, Issue 3
June 2024
Pages 322-339
  • Receive Date: 06 March 2024
  • Revise Date: 20 March 2024
  • Accept Date: 25 March 2024