Numerical Prediction of Deflection and Stress Responses of Functionally Graded Structure for Grading Patterns (Power-Law, Sigmoid, and Exponential) and Variable Porosity (Even/Uneven)

Document Type : Article

Authors

1 Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela { 769008, Odisha, India

2 Department of Mechanical Engineering, Madanapalle Institute of Technology and Science, Madanapalle { 517325, Andhra, Pradesh, India

3 School of Mechanical Engineering, KIIT (Deemed to be University) Bhubaneswar, Bhubaneswar { 751024, Odisha, India

Abstract

The finite element solutions of static deflection and stress values are obtained in this article for the functionally graded structure considering variable grading patterns (power-law, sigmoid and exponential) including the porosity effect. The unknown values are obtained computationally via a customized computer code with the help of cubic-order displacement functions considering the varied distribution of porosity (even and uneven) through the panel thickness. Also, the values are simulated through design software (ANSYS) to establish the present numerical solution accuracy. The comparison as well as the element sensitivity behaviour of the present numerical model verified by solving different kinds of numerical examples available in the published domain. Lastly, the effect of several influential geometry relevant parameters (aspect ratio, curvature ratio, thickness ratio, porosity index, type of porosity, power-law exponent, geometrical configuration and support conditions) affecting the structural stiffness and the corresponding outcomes (deflection and stress) of the FG structure are computed through the presently derived numerical model.

Keywords

References

References
1.        Chi, S.-H. and Chung, Y.-L., “Mechanical behavior of functionally graded material plates under transverse load — Part I : Analysis”, Int. J. Solids Struct., 43, pp. 3657–3674 (2006).
2.        Wang, Y. Q. and Zu, J. W., “Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment”, Aerosp. Sci. Technol., 69, pp. 550–562 (2017).
3.        Kashtalyan, M., “Three-dimensional elasticity solution for bending of functionally graded rectangular plates”, Eur. J. Mech. A/Solids, 23(5), pp. 853–864 (2004).
4.        Zenkour, A. M., “Generalized shear deformation theory for bending analysis of functionally graded plates”, Appl. Math. Model., 30(1), pp. 67–84 (2006).
5.        Chung, Y.-L. and Chen, W.-T., “Bending behavior of FGM-coated and FGM-undercoated plates with two simply supported opposite edges and two free edges”, Compos. Struct., 81, pp. 157–167 (2007).
6.        Ben-Oumrane, S., Abedlouahed, T., Ismail, M., Mohamed, B. B., Mustapha, M., and Abbas, A. B. El, “A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams”, Comput. Mater. Sci., 44(4), pp. 1344–1350 (2009).
7.        Bhandari, M. and Purohit, K., “Static response of functionally graded material plate under transverse load for varying aspect ratio”, Int. J. Met., 2014, pp. 1–11 (2014).
8.        Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T., and Krplin, B., “Thermo-mechanical bending of functionally graded plates”, J. Therm. Stress., 31(3), pp. 286–308 (2008).
9.        Filippi, M., Carrera, E., and Zenkour, A. M., “Static analyses of FGM beams by various theories and finite elements”, Compos. Part B Eng., 72, pp. 1–9 (2015).
10.      Thai, H.-T. and Choi, D.-H., “A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates”, Compos. Struct., 101, pp. 332–340 (2013).
11.      Talha, M. and Singh, B. N., “Static response and free vibration analysis of FGM plates using higher order shear deformation theory”, Appl. Math. Model., 34(12), pp. 3991–4011 (2010).
12.      Zhao, Z., Feng, C., Wang, Y., and Yang, J., “Bending and vibration analysis of functionally graded trapezoidal nanocomposite plates reinforced with graphene nanoplatelets (GPLs)”, Compos. Struct., 180, pp. 799–808 (2017).
13.      Bellifa, H., Benrahou, K. H., Hadji, L., Houari, M. S. A., and Tounsi, A., “Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position”, J. Brazilian Soc. Mech. Sci. Eng., 38(1), pp. 265–275 (2016).
14.      Sherafat, M. H., Ovesy, H. R., and Ghannadpour, S. A. M., “Buckling analysis of functionally graded plates under mechanical loading using higher order functionally graded strip”, Int. J. Struct. Stab. Dyn., 13(6), pp. 1–13 (2013).
15.      Thai, H.-T., Vo, T. P., Bui, T. Q., and Nguyen, T.-K., “A quasi-3D hyperbolic shear deformation theory for functionally graded plates”, Acta Mech., 225(3), pp. 951–964 (2014).
16.      Vu, T. Van, Nguyen, N. H., Khosravifard, A., Hematiyan, M. R., Tanaka, S., and Bui, T. Q., “A simple FSDT-based meshfree method for analysis of functionally graded plates”, Eng. Anal. Bound. Elem., 79, pp. 1–12 (2017).
17.      Mirzaei, M. and Kiani, Y., “Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout”, Beilstein J. Nanotechnol., 7(1), pp. 511–523 (2016).
18.      Kiani, Y., “Free vibration of FG-CNT reinforced composite spherical shell panels using Gram-Schmidt shape functions”, Compos. Struct., 159, pp. 368–381 (2017).
19.      Hajmohammad, M. H., Azizkhani, M. B., and Kolahchi, R., “Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis”, Int. J. Mech. Sci., 137, pp. 205–213 (2018).
20.      Hajmohammad, M. H., Farrokhian, A., and Kolahchi, R., “Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory”, Aerosp. Sci. Technol. Technol., 78, pp. 260–270 (2018).
21.      Besseghier, A., Houari, M. S. A., Tounsi, A., and Mahmoud, S. R., “Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory”, Smart Struct. Syst., 19(6), pp. 601–614 (2017).
22.      Abualnour, M., Houari, M. S. A., Tounsi, A., Bedia, E. A. A., and Mahmoud, S. R., “A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates”, Compos. Struct., 184, pp. 688–697 (2018).
23.      Thai, C. H., Tran, T. D., and Phung-Van, P., “A size-dependent moving Kriging meshfree model for deformation and free vibration analysis of functionally graded carbon nanotube-reinforced composite nanoplates”, Eng. Anal. Bound. Elem., 115, pp. 52–63 (2020).
24.      Belkhodja, Y., Ouinas, D., Zaoui, F. Z., and Fekirini, H., “An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates”, Adv. Compos. Lett., 29, p. 096369351987573 (2020).
25.      Do, V. T., Pham, V. V., and Nguyen, H. N., “On the development of refined plate theory for static bending behavior of functionally graded plates”, Math. Probl. Eng., 2020, pp. 1–13 (2020).
26.      Zhang, P., Qing, H., and Gao, C., “Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress-driven nonlocal integral model”, Compos. Struct., p. 112362 (2020).
27.      Ghassabi, M., Talebitooti, R., and Zarastvand, M. R., “State vector computational technique for three-dimensional acoustic sound propagation through doubly curved thick structure”, Comput. Methods Appl. Mech. Eng., 352, pp. 324–344 (2019).
28.      Ghassabi, M., Zarastvand, M. R., and Talebitooti, R., “Investigation of state vector computational solution on modeling of wave propagation through functionally graded nanocomposite doubly curved thick structures”, Eng. Comput., pp. 1-17 (2019).
29.      Talebitooti, R., Zarastvand, M., and Rouhani, A. S., “Investigating Hyperbolic Shear Deformation Theory on vibroacoustic behavior of the infinite Functionally Graded thick plate”, Lat. Am. J. Solids Struct., 16(1), pp. 1–17 (2019).
30.      Talebitooti, R., Johari, V., and Zarastvand, M., “Wave transmission across laminated composite plate in the subsonic flow Investigating Two-variable Refined Plate Theory”, Lat. Am. J. Solids Struct., 15(5) (2018).
31.      Talebitooti, R., Zarastvand, M., and Gohari, H., “Investigation of power transmission across laminated composite doubly curved shell in the presence of external flow considering shear deformation shallow shell theory”, J. Vib. Control, 24(19), pp. 4492–4504 (2018).
32.      Talebitooti, R. and Zarastvand, M. R., “Vibroacoustic behavior of orthotropic aerospace composite structure in the subsonic flow considering the Third order Shear Deformation Theory”, Aerosp. Sci. Technol., 75, pp. 227–236 (2018).
33.      Talebitooti, R., Zarastvand, M. R., and Gohari, H. D., “The influence of boundaries on sound insulation of the multilayered aerospace poroelastic composite structure”, Aerosp. Sci. Technol., 80, pp. 452–471 (2018).
34.      Balubaid, M., Tounsi, A., Dakhel, B., and Mahmoud, S. R., “Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory”, Comput. Concr., 24(6), pp. 579–586 (2019).
35.      Tounsi, A., Al-Dulaijan, S. U., Al-Osta, M. A., Chikh, A., Al-Zahrani, M. M., Sharif, A., and Tounsi, A., “A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation”, Steel Compos. Struct., 34(4), pp. 511–524 (2020).
36.      Bellal, M., Hebali, H., Heireche, H., Bousahla, A. A., Tounsi, A., Bourada, F., Mahmoud, S. R., Bedia, E. A. A., and Tounsi, A., “Buckling behavior of a single-layered graphene sheet resting on viscoelastic medium via nonlocal four-unknown integral model”, Steel Compos. Struct., 34(5), pp. 643–655 (2020).
37.      Rahmani, M. C., Kaci, A., Bousahla, A. A., Bourada, F., Tounsi, A., Bedia, E. A. A., Mahmoud, S. R., Benrahou, K. H., and Tounsi, A., “Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory”, Comput. Concr., 25(3), pp. 225–244 (2020).
38.      Chaabane, L. A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F. Z., Tounsi, A., Derras, A., Bousahla, A. A., and Tounsi, A., “Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation”, Struct. Eng. Mech., 71(2), pp. 185–196 (2019).
39.      Boutaleb, S., Benrahou, K. H., Bakora, A., Algarni, A., Bousahla, A. A., Tounsi, A., Tounsi, A., and Mahmoud, S. R., “Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT”, Adv. Nano Res., 7(3), pp. 191–208 (2019).
40.      Boussoula, A., Boucham, B., Bourada, M., Bourada, F., and Tounsi, A., “A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates”, Smart Struct. Syst., 25(2), pp. 197–218 (2020).
41.      Refrafi, S., Bousahla, A. A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Bedia, E. A. A., Mahmoud, S. R., Benrahou, K. H., and Tounsi, A., “Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations”, Comput. Concr., 25(4), pp. 311–325 (2020).
42.      Motezaker, M., Jamali, M., and Kolahchi, R., “Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory”, J. Comput. Appl. Math., 369, p. 112625 (2020).
43.      Kolahchi, R., Hosseini, H., Fakhar, M. H., Taherifar, R., and Mahmoudi, M., “A numerical method for magneto-hygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions”, Comput. Math. with Appl., 78(6), pp. 2018–2034 (2019).
44.      Keshtegar, B., Farrokhian, A., Kolahchi, R., and Trung, N.-T., “Dynamic stability response of truncated nanocomposite conical shell with magnetostrictive face sheets utilizing higher order theory of sandwich panels”, Eur. J. Mech. - A/Solids, 82, p. 104010 (2020).
45.      Farokhian, A. and Kolahchi, R., “Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs”, Struct. Eng. Mech., 73(5), pp. 555–563 (2020).
46.      Keshtegar, B., Bagheri, M., Meng, D., Kolahchi, R., and Trung, N.-T., “Fuzzy reliability analysis of nanocomposite ZnO beams using hybrid analytical-intelligent method”, Eng. Comput. pp. 1-16 (2020).
47.      Chen, D., Yang, J., and Kitipornchai, S., “Elastic buckling and static bending of shear deformable functionally graded porous beam”, Compos. Struct., 133, pp. 54–61 (2015).
48.      Kim, J., Żur, K. K., and Reddy, J. N., “Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates”, Compos. Struct., 209, pp. 879–888 (2019).
49.      She, G. L., Yuan, F. G., Ren, Y. R., Liu, H. B., and Xiao, W. S., “Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory”, Compos. Struct., 203, pp. 614–623 (2018).
50.      Sahmani, S., Aghdam, M. M., and Rabczuk, T., “Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory”, Compos. Struct., 186, pp. 68–78 (2018).
51.      Berghouti, H., Bedia, E. A. A., Benkhedda, A., and Tounsi, A., “Vibration analysis of nonlocal porous nanobeams made of functionally graded material”, Adv. Nano Res., 7(5), pp. 351–364 (2019).
52.      Bourada, F., Bousahla, A. A., Bourada, M., Azzaz, A., Zinata, A., and Tounsi, A., “Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory”, Wind Struct., 28(1), pp. 19–30 (2019).
53.      Addou, F. Y., Meradjah, M., Bousahla, A. A., Benachour, A., Bourada, F., Tounsi, A., and Mahmoud, S. R., “Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT”, Comput. Concr., 24(4), pp. 347–367 (2019).
54.      Kaddari, M., Kaci, A., Bousahla, A. A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E. A. A., and Al-Osta, M. A., “A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis”, Comput. Concr., 25(1), pp. 37–57 (2020).
55.      Amir, M. and Talha, M., “Nonlinear vibration characteristics of shear deformable functionally graded curved panels with porosity including temperature effects”, Int. J. Press. Vessel. Pip., 172, pp. 28–41 (2019).
56.      Avcar, M., “Free vibration of imperfect sigmoid and power law functionally graded beams”, Steel Compos. Struct., 30(6), pp. 603–615 (2019).
57.      Kar, V. R. and Panda, S. K., “Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method”, J. Vib. Control, 22(7), pp. 1935–1949 (2016).
58.      Reddy, J. N., “Mechanics of Laminated Composite Plates and Shells: Theory and Analysis”, 2nd Edn., CRC Press, New York (2004).
59.      Cook, R. D., Malkus, D. S., Plesha, M. E., and Witt, R. J., “Concepts and Applications of Finite Element Analysis”, 4th Edn., John Wiley and Sons, Singapore (2009).
60.      Daouadji, T. H., Tounsi, A., and Bedia, E. A. A., “Analytical solution for bending analysis of functionally graded plates”, Sci. Iran., 20(3), pp. 516–523 (2013).
Scientia Iranica
Volume 28, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2021
Pages 811-829

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History

  • Receive Date: 20 April 2020
  • Revise Date: 19 May 2020
  • Accept Date: 29 June 2020

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