Browse > Article
http://dx.doi.org/10.12989/acc.2022.13.5.377

Investigating nonlinear static behavior of hyperelastic plates using three-parameter hyperelastic model  

Afshari, Behzad Mohasel (Fidar Project Qaem Company)
Mirjavadi, Seyed Sajad (Department of Mechanical and Industrial Engineering, Qatar University)
Barati, Mohammad Reza (Respina Lubricant Supply Company)
Publication Information
Advances in concrete construction / v.13, no.5, 2022 , pp. 377-384 More about this Journal
Abstract
The present paper deals with nonlinear deflection analysis of hyperelastic plates rested on elastic foundation and subject to a transverse point force. For modeling of hyperelastic material, three-parameter Ishihara model has been employed. The plate formulation is based on classic plate theory accounting for von-Karman geometric nonlinearity. Therefore, both material and geometric nonlinearities have been considered based on Ishihara hyperelastic plate model. The governing equations for the plate have been derived based on Hamilton's rule and then solved via Galerkin's method. Obtained results show that material parameters of hyperelastic material play an important role in defection analysis. Also, the effects of foundation parameter and load location on plate deflections will be discussed.
Keywords
deflection; Galerkin's method; hyperelastic material; nonlinear analysis; plate bending;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
연도 인용수 순위
1 Ogden, R.W., Saccomandi, G. and Sgura, I. (2004), "Fitting hyperelastic models to experimental data", Comput. Mech., 34(6), 484-502. https://doi.org/10.1007/s00466-004-0593-y.   DOI
2 Shahzad, M., Kamran, A., Siddiqui, M. Z. and Farhan, M. (2015), "Mechanical characterization and FE modelling of a hyperelastic material", Mater. Res., 18(5), 918-924. https://doi.org/10.1590/1516-1439.320414.   DOI
3 Steinmann, P., Hossain, M. and Possart, G. (2012), "Hyperelastic models for rubber-like materials: Consistent tangent operators and suitability for Treloar's data", Archiv. Appl. Mech., 82(9), 1183-1217. https://doi.org/10.1007/s00419-012-0610-z.   DOI
4 Wang, Y., Ding, H. and Chen, L. Q. (2019), "Vibration of axially moving hyperelastic beam with finite deformation", Appl. Math. Model., 71, 269-285. https://doi.org/10.1016/j.apm.2019.02.011.   DOI
5 Barforooshi, S.D. and Mohammadi, A.K. (2016), "Study neo-Hookean and Yeoh hyper-elastic models in dielectric elastomer-based micro-beam resonators", Latin Am. J. Solid. Struct., 13(10), 1823-1837. https://doi.org/10.1590/1679-78252432.   DOI
6 Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081.   DOI
7 Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009.   DOI
8 Du Toit, V. (2018), "Characterising material models for silicone-rubber using an inverse finite element model updating method", Doctoral Dissertation of Philosophy, Stellenbosch University.
9 Breslavsky, I.D., Amabili, M. and Legrand, M. (2014), "Nonlinear vibrations of thin hyperelastic plates", J. Sound Vib., 333(19), 4668-4681. https://doi.org/10.1016/j.jsv.2014.04.028.   DOI
10 Batou, B., Nebab, M., Bennai, R., Atmane, H.A., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.   DOI
11 Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2021), "Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading", Struct. Eng. Mech., 78(1), 15-22. http://doi.org/10.12989/sem.2021.78.1.015.   DOI
12 Horgan, C.O. and Saccomandi, G. (2006), "Phenomenological hyperelastic strain-stiffening constitutive models for rubber", Rubber Chem. Tech., 79(1), 152-169. https://doi.org/10.5254/1.3547924.   DOI
13 Marckmann, G. and Verron, E. (2006), "Comparison of hyperelastic models for rubber-like materials", Rubber Chem. Tech., 79(5), 835-858. https://doi.org/10.5254/1.3547969.   DOI
14 Ahmed, R.A., Mustafa, N.M., Faleh, N.M. and Fenjan, R.M. (2020), "Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method", Struct. Eng. Mech., 76(3), 413-420. http://doi.org/10.12989/sem.2020.76.3.413.   DOI
15 Ali, A., Hosseini, M. and Sahari, B.B. (2010), "A review and comparison on some rubber elasticity models", J. Sci. Indust. Res., 69(7), 495-500.
16 Mirjavadi, S.S., Forsat, M. and Badnava, S. (2019), "Nonlinear modeling and dynamic analysis of bioengineering hyper-elastic tubes based on different material models", Biomech. Model. Mechanobio., 1-13. https://doi.org/10.1007/s10237-019-01265-8.   DOI
17 Soares, R.M. and Goncalves, P.B. (2018), "Nonlinear vibrations of a rectangular hyperelastic membrane resting on a nonlinear elastic foundation", Meccanica, 53(4-5), 937-955. https://doi.org/10.1007/s11012-017-0755-5.   DOI
18 Barati, M.R. and Shahverdi, H. (2018), "Nonlinear vibration of nonlocal four-variable graded plates with porosities implementing homotopy perturbation and Hamiltonian methods", Acta Mechanica, 229(1), 343-362. https://doi.org/10.1007/s00707-017-1952-y.   DOI
19 Martins, P.A.L.S., Natal Jorge, R.M. and Ferreira, A.J.M. (2006), "A comparative study of several material models for prediction of hyperelastic properties: Application to silicone-rubber and soft tissues", Strain, 42(3), 135-147. https://doi.org/10.1111/j.1475-1305.2006.00257.x.   DOI
20 Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.   DOI
21 Mohammadi, A.K. and Barforooshi, S.D. (2017), "Nonlinear forced vibration analysis of dielectric-elastomer based micro-beam with considering Yeoh hyper-elastic model", Latin Am. J. Solid. Struct., 14(4), 643-656. http://doi.org/10.1590/1679-78253324.   DOI