Skip to main content
SpringerLink
Log in

NURBS based thermoelastic behaviour of thin functionally graded sigmoidal (TFGS) porous plate resting on variable Winkler's foundation

  • Published:
International Journal of Mechanics and Materials in Design Aims and scope Submit manuscript

Abstract

In this current study, thermoelastic static and vibration analysis of the thin functionally graded sigmoidal porous plate subjected using higher-order NURBS-based Isogeometric analysis has been performed. The variation of thermomechanical material properties of this plate is using modified power and sigmoid law. To formulate the mathematical model for plate the Kirchhoff–Love theory-based displacement fields with the virtual work principle and high-order continuity of the NURBS basis functions based isogeometric analysis are employed. Convergence and assessment study has been done to verify the effectiveness and precision of the current approach. The effect of the porosity index, material gradient index, boundary conditions, thermal loading and geometry on the deflection, vibration frequency and detailed investigation of mode shapes. From the analysis, it has been noted that normalized frequency decreases and normalized central deflection increase when the gradient index of the material rises. The findings of this analysis can be utilized for members with extremely less thickness, such as turbine plates and blades, nuclear reactor vessels, and many other machine components made of porous functionally graded material materials.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Akavci, S.S., Tanrikulu, A.H.: Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories. Compos. B Eng. 83, 203–215 (2015)

    Article  Google Scholar 

  • Attia, A., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R.: Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories. Steel Compos. Struct. 18(1), 187–212 (2015)

    Article  Google Scholar 

  • Baferani, A.H., Saidi, A.R., Jomehzadeh, E.: An exact solution for free vibration of thin functionally graded rectangular plates. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 225(3), 526–536 (2011)

    Article  MATH  Google Scholar 

  • Barron, R.F., Barron, B.R.: Design for Thermal Stresses. Wiley, New York (2011)

    Book  MATH  Google Scholar 

  • Bedroud, M., Nazemnezhad, R., Hosseini-Hashemi, S.: Axisymmetric/asymmetric buckling of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity. Meccanica 50(7), 1791–1806 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R.: On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model. Steel Compos. Struct. 18(4), 1063–1081 (2015)

    Article  Google Scholar 

  • Boggarapu, V., Gujjala, R., Ojha, S., Acharya, S., Chowdary, S., Kumar Gara, D.: State of the art in functionally graded materials. Compos. Struct. 262, 113596 (2021)

    Article  Google Scholar 

  • Cottrell, J.A., Hughes, T.J., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, New York (2009)

    Book  MATH  Google Scholar 

  • Cottrell, J.A., Reali, A., Bazilevs, Y., Hughes, T.J.: Isogeometric analysis of structural vibrations. Comput. Methods Appl. Mech. Eng. 195(41–43), 5257–5296 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Enab, T.A.: Stress concentration analysis in functionally graded plates with elliptic holes under biaxial loadings. Ain Shams Eng. J. 5(3), 839–850 (2014)

    Article  Google Scholar 

  • Harsha, A., Kumar, P.: Thermoelectric elastic analysis of bi-directional three-layer functionally graded porous piezoelectric (FGPP) plate resting on elastic foundation. Forces Mech. 8, 100112 (2022)

    Article  Google Scholar 

  • Hosseini-Hashemi, S., Bedroud, M., Nazemnezhad, R.: An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity. Compos. Struct. 103, 108–118 (2013)

    Article  MATH  Google Scholar 

  • Hosseini-Hashemi, S., Fadaee, M., Atashipour, S.R.: A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates. Int. J. Mech. Sci. 53(1), 11–22 (2011)

    Article  Google Scholar 

  • Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H., Omidi, M.: Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl. Math. Model. 34(5), 1276–1291 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Huang, X.L., Shen, H.S.: Nonlinear vibration and dynamic response of functionally graded plates in thermal environments. Int. J. Solids Struct. 41(9–10), 2403–2427 (2004)

    Article  MATH  Google Scholar 

  • Hughes, T.J., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194(39–41), 4135–4195 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • Kumar, P., Harsha, S.P.: Response analysis of hybrid functionally graded material plate subjected to thermo-electro-mechanical loading. Proc. Inst. Mech. Eng. L J. Mater. Des. Appl. 235(4), 813–827 (2021a)

    Google Scholar 

  • Kumar, P., Harsha, S.P.: Vibration response analysis of exponential functionally graded piezoelectric (EFGP) plate subjected to thermo-electro-mechanical load. Compos. Struct. 267, 113901 (2021b)

    Article  Google Scholar 

  • Kumar, P., Harsha, S.P.: Vibration response analysis of PZT-4/PZT-5H based functionally graded tapered plate subjected to electro-mechanical loading. Mech. Res. Commun. 116, 103765 (2021c)

    Article  Google Scholar 

  • Kumar, P., Harsha, A.: Vibration response analysis of the bi-directional porous functionally graded piezoelectric (BD-FGP) plate. Mech. Based Des. Struct. Mach. (2022). https://doi.org/10.1080/15397734.2022.2099418

    Article  Google Scholar 

  • Kumar, P., Harsha, S.P.: Static analysis of porous core functionally graded piezoelectric (PCFGP) sandwich plate resting on the Winkler/Pasternak/Kerr foundation under thermo-electric effect. Mater. Today Commun. (2022a). https://doi.org/10.1016/j.mtcomm.2022.103929

    Article  Google Scholar 

  • Kumar, P., Harsha, S.P.: Response analysis of functionally graded piezoelectric plate resting on elastic foundation under thermo-electro environment. J. Compos. Mater. 56(24), 3749–3767 (2022b)

    Article  Google Scholar 

  • Kumar, P., Harsha, S.P.: Electroelastic static and vibration response analysis of sigmoid PZT-5A/Pt based smart functionally graded (SFG) plate. Int. J. Struct. Stab. Dyn. (2022c). https://doi.org/10.1142/S0219455422501553

    Article  Google Scholar 

  • Kumar, P., Harsha, S.P.: Static, buckling and vibration response analysis of three-layered functionally graded piezoelectric plate under thermo-electric mechanical environment. J. Vib. Eng. Technol. (2022d). https://doi.org/10.1007/s42417-022-00467-2

    Article  Google Scholar 

  • Kumar, P., Harsha, S.P.: Dynamic analysis of porosity dependent functionally graded sigmoid piezoelectric (FGSP) plate. Structures 46, 564 (2022e)

    Article  Google Scholar 

  • Kumar, V., Singh, S.J., Saran, V.H., Harsha, S.P.: Vibration response analysis of tapered porous FGM plate resting on elastic foundation. Int. J. Struct. Stab. Dyn. (2022). https://doi.org/10.1142/S0219455423500244

    Article  Google Scholar 

  • Lall, P., Harsha, M., Goebel, K.: Method for Determination of Accrued Damage and Remaining Life During Field-Usage in Lead-Free Electronics, SMTAI (2012a)

  • Lall, P., Harsha, M., Goebel, K., Suhling, J.: Sustained damage and remaining useful life assessment in leadfree electronics subjected to sequential multiple thermal environments. ECTC (2012b)

  • Li, X., Zhang, J., Zheng, Y.: NURBS-based isogeometric analysis of beams and plates using high order shear deformation theory. Math. Probl. Eng. (2013)

  • Minh, P.P., Duc, N.D.: The effect of cracks and thermal environment on free vibration of FGM plates. Thin-Walled Struct. 159, 107291 (2021)

    Article  Google Scholar 

  • Nami, M.R., Janghorban, M.: Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant. Compos. Struct. 111, 349–353 (2014)

    Article  Google Scholar 

  • Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S., Rabczuk, T.: Size-dependent free flexural vibration behavior of functionally graded nanoplates. Comput. Mater. Sci. 65, 74–80 (2012)

    Article  Google Scholar 

  • Nguyen-Xuan, H., Tran, L.V., Thai, C.H., Kulasegaram, S., Bordas, S.P.A.: Isogeometric analysis of functionally graded plates using a refined plate theory. Compos. B Eng. 64, 222–234 (2014)

    Article  Google Scholar 

  • Nguyen-Xuan, H., Tran, L.V., Thai, C.H., Nguyen-Thoi, T.: Analysis of functionally graded plates by an efficient finite element method with node-based strain smoothing. Thin-Walled Struct. 54, 1–18 (2012)

    Article  Google Scholar 

  • Pigel, L., Tiller, W.: The NURBS book (1997)

  • Pradhan, K.K., Chakraverty, S.: Free vibration of functionally graded thin elliptic plates with various edge supports. Struct. Eng. Mech. Int. J. 53(2), 337–354 (2015)

    Article  Google Scholar 

  • Prakash, A., Kumar, S.R., Verma, R.: Vibration analysis of functionally graded materials for cylinder liner used in agricultural engine part. Open Agric. 4(1), 258–266 (2019)

    Article  Google Scholar 

  • Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells. CRC Press, Boca Raton (2006)

    Book  Google Scholar 

  • Reddy, J.N., Chin, C.D.: Thermomechanical analysis of functionally graded cylinders and plates. J. Therm. Stresses 21(6), 593–626 (1998)

    Article  Google Scholar 

  • Singh, S.J., Harsha, S.P.: Thermal buckling of porous symmetric and non-symmetric sandwich plate with homogenous core and S-FGM face sheets resting on Pasternak foundation. Int. J. Mech. Mater. Des. 16(4), 707–731 (2020)

    Article  Google Scholar 

  • Thai, H.T., Kim, S.E.: A review of theories for the modeling and analysis of functionally graded plates and shells. Compos. Struct. 128, 70–86 (2015)

    Article  Google Scholar 

  • Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H.: Isogeometric analysis of functionally graded plates using higher-order shear deformation theory. Compos. B Eng. 51, 368–383 (2013)

    Article  Google Scholar 

  • Valizadeh, N., Natarajan, S., Gonzalez-Estrada, O.A., Rabczuk, T., Bui, T.Q., Bordas, S.P.: NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter. Compos. Struct. 99, 309–326 (2013)

    Article  Google Scholar 

  • Wang, B., Zhou, S., Zhao, J., Chen, X.: A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory. Eur. J. Mech. A Solids 30(4), 517–524 (2011)

    Article  MATH  Google Scholar 

  • Woodward, B., Kashtalyan, M.: Performance of functionally graded plates under localised transverse loading. Compos. Struct. 94(7), 2254–2262 (2012)

    Article  Google Scholar 

  • Xiao, H.T., Yue, Z.Q.: Stresses and displacements in functionally graded materials of semi-infinite extent induced by rectangular loadings. Materials 5(2), 210–226 (2012)

    Article  Google Scholar 

  • Yin, S., Hale, J.S., Yu, T., Bui, T.Q., Bordas, S.P.: Isogeometric locking-free plate element: a simple first order shear deformation theory for functionally graded plates. Compos. Struct. 118, 121–138 (2014)

    Article  Google Scholar 

  • Yin, S., Yu, T., Liu, P.: Free vibration analyses of FGM thin plates by isogeometric analysis based on classical plate theory and physical neutral surface. Adv. Mech. Eng. 5, 634584 (2013)

    Article  Google Scholar 

  • Zare, M., Nazemnezhad, R., Hosseini-Hashemi, S.: Natural frequency analysis of functionally graded rectangular nanoplates with different boundary conditions via an analytical method. Meccanica 50(9), 2391–2408 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, L.W., Cui, W.C., Liew, K.M.: Vibration analysis of functionally graded carbon nanotube reinforced composite thick plates with elastically restrained edges. Int. J. Mech. Sci. 103, 9–21 (2015b)

    Article  Google Scholar 

  • Zhang, B., He, Y., Liu, D., Shen, L., Lei, J.: An efficient size-dependent plate theory for bending, buckling and free vibration analyses of functionally graded microplates resting on elastic foundation. Appl. Math. Model. 39(13), 3814–3845 (2015a)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical and Industrial Engineering Department, IIT Roorkee, Roorkee, India

    Anand Prakash, Pawan Kumar, V. H. Saran & S. P. Harsha

Authors
  1. Anand Prakash
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pawan Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. H. Saran
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. P. Harsha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. P. Harsha.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing fnancial interests or personal relationships that could have appeared to infuence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

Additional results for the discussion in Sects. 3.3.1 and 3.3.2 are given in Tables 8a, b, 9 and 10.

Table 8 First five modes of normalized natural frequencies for rectangular TFGS porous plate under thermal loading (a/h = 100)
Full size table
Table 9 Normalized central deflection of square TFGS porous plate
Full size table
Table 10 Normalized central deflection of rectangular TFGS porous plate
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prakash, A., Kumar, P., Saran, V.H. et al. NURBS based thermoelastic behaviour of thin functionally graded sigmoidal (TFGS) porous plate resting on variable Winkler's foundation. Int J Mech Mater Des 19, 831–860 (2023). https://doi.org/10.1007/s10999-023-09654-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10999-023-09654-9

Keywords

Search

Navigation