Skip to main content
SpringerLink
Log in

Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

This study presents the size-dependent nonlinear thermal postbuckling characteristics of a porous functionally graded material (PFGM) microplate with a central cutout with various shapes using isogeometric numerical technique incorporating non-uniform rational B-splines. To construct the proposed non-classical plate model, the nonlocal strain gradient continuum elasticity is adopted on the basis of a hybrid quasi-three-dimensional (3D) plate theory under through-thickness deformation conditions by only four variables. By taking a refined power-law function into account in conjunction with the Touloukian scheme, the temperature-porosity-dependent material properties are extracted. With the aid of the assembled isogeometric-based finite element formulations, nonlocal strain gradient thermal postbuckling curves are acquired for various boundary conditions as well as geometrical and material parameters. It is portrayed that for both size dependency types, by going deeper in the thermal postbuckling domain, gaps among equilibrium curves associated with various small scale parameter values get lower, which indicates that the pronounce of size effects reduces by going deeper in the thermal postbuckling regime. Moreover, we observe that the central cutout effect on the temperature rise associated with the thermal postbuckling behavior in the presence of the effect of strain gradient size and absence of nonlocality is stronger compared with the case including nonlocality in absence of the strain gradient small scale effect.

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

Similar content being viewed by others

References

  1. SAHMANI, S. and SAFAEI, B. Large-amplitude oscillations of composite conical nanoshells with in-plane heterogeneity including surface stress effect. Applied Mathematical Modelling, 89, 1792–1813 (2021)

    Article  MathSciNet  Google Scholar 

  2. FAN, F., XU, Y., SAHMANI, S., and SAFAEI, B. Modified couple stress-based geometrically nonlinear oscillations of porous functionally graded microplates using NURBS-based isogeometric approach. Computer Methods in Applied Mechanics and Engineering, 372, 113400 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  3. SAFAEI, B. The effect of embedding a porous core on the free vibration behavior of laminated composite plates. Steel and Composite Structures, 35(5), 659–670 (2020)

    Google Scholar 

  4. YUAN, Y., ZHAO, X., ZHAO, Y., SAHMANI, S., and SAFAEI, B. Dynamic stability of nonlocal strain gradient FGM truncated conical microshells integrated with magnetostrictive facesheets resting on a nonlinear viscoelastic foundation. Thin-Walled Structures, 159, 107249 (2021)

    Article  Google Scholar 

  5. JIA, L., LIU, B., ZHAO, Y., CHEN, W., MOU, D., FU, J., WANG, Y., XIN, W., and ZHAO, L. Structure design of MoS2@Mo2C on nitrogen-doped carbon for enhanced alkaline hydrogen evolution reaction. Journal of Materials Science, 55(34), 16197–16210 (2020)

    Article  Google Scholar 

  6. GARCÍA-SALABERRI, P. A. Modeling diffusion and convection in thin porous transport layers using a composite continuum-network model: application to gas diffusion layers in polymer electrolyte fuel cells. International Journal of Heat and Mass Transfer, 167, 120824 (2021)

    Article  Google Scholar 

  7. CASSIO, F., LORRAIN, N., PIRASTEH, P., POFFO, L., LEMAITRE, J., HARDY, I., and GUENDOUZ, M. Porosity calibration in a 4-layer porous silicon structure to fabricate a micro-resonator with well-defined refractive indices and dedicated to biosensing applications. Optical Materials, 110, 110468 (2020)

    Article  Google Scholar 

  8. XIE, B., SAHMANI, S., SAFAEI, B., and XU, B. Nonlinear secondary resonance of FG porous silicon nanobeams under periodic hard excitations based on surface elasticity theory. Engineering with Computers, 1–24 (2020)

  9. HWANG, J., KIM, Y., YANG, H., and OH, J. H. Fabrication of hierarchically porous structured PDMS composites and their application as a flexible capacitive pressure sensor. Composites Part B: Engineering, 108607 (2021)

  10. LIN, J., HU, J., WANG, W., LIU, K., ZHOU, C., LIU, Z., KONG, S., LIN, S., DENG, Y., and GUO, Z. Thermo and light-responsive strategies of smart titanium-containing composite material surface for enhancing bacterially anti-adhesive property. Chemical Engineering Journal, 407, 125783 (2021)

    Article  Google Scholar 

  11. AREFI, M., MOHAMMAD-REZAEI BIDGOLI, E., DIMITRI, R., and TORNABENE, F. Free vibrations of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets. Aerospace Science and Technology, 81, 108–117 (2018)

    Article  Google Scholar 

  12. 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. Composite Structures, 186, 68–78 (2018)

    Article  Google Scholar 

  13. SAHMANI, S., AGHDAM, M. M., and RABCZUK, T. Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs. Composite Structures, 198, 51–62 (2018)

    Article  Google Scholar 

  14. TOGUN, N. and BAǦDATLI, S. M. Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory. Composites Part B: Engineering, 97, 255–262 (2016)

    Article  Google Scholar 

  15. SAHMANI, S. and SAFAEI, B. Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded micro/nano-beams. Applied Mathematical Modelling, 82, 336–358 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. FAN, L., SAHMANI, S., and SAFAEI, B. Couple stress-based dynamic stability analysis of functionally graded composite truncated conical microshells with magnetostrictive facesheets embedded within nonlinear viscoelastic foundations. Engineering with Computers, 1–21 (2020) https://doi.org/10.1007/s00366-020-01182-w

  17. YI, H., SAHMANI, S., and SAFAEI, B. On size-dependent large-amplitude free oscillations of FGPM nanoshells incorporating vibrational mode interactions. Archives of Civil and Mechanical Engineering, 20(2), 48 (2020)

    Article  Google Scholar 

  18. YANG, X., SAHMANI, S., and SAFAEI, B. Postbuckling analysis of hydrostatic pressurized FGM microsized shells including strain gradient and stress-driven nonlocal effects. Engineering with Computers, 1–16 (2020) https://doi.org/10.1007/s00366-019-00901-2

  19. YUAN, Y., ZHAO, K., SAHMANI, S., and SAFAEI, B. Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes. Applied Mathematics and Mechanics (English Edition), 41(4), 587–604 (2020) https://doi.org/10.1007/s10483-020-2600-6

    Article  MathSciNet  MATH  Google Scholar 

  20. FAN, F., ZHAO, K., SAHMANI, S., and SAFAEI, B. Nonlinear oscillations of composite conical microshells with in-plane heterogeneity based upon a couple stress-based shell model. Thin-Walled Structures, 154, 106841 (2020)

    Article  Google Scholar 

  21. YUAN, Y., ZHAO, K., HAN, Y., SAHMANI, S., and SAFAEI, B. Nonlinear oscillations of composite conical microshells with in-plane heterogeneity based upon a couple stress-based shell model. Thin-Walled Structures, 154, 106857 (2020)

    Article  Google Scholar 

  22. YUAN, Y., ZHAO, K., ZHAO, Y., SAHMANI, S., and SAFAEI, B. Couple stress-based nonlinear buckling analysis of hydrostatic pressurized functionally graded composite conical microshells. Mechanics of Materials, 148, 103507 (2020)

    Article  Google Scholar 

  23. LI, Q., XIE, B., SAHMANI, S., and SAFAEI, B. Surface stress effect on the nonlinear free vibrations of functionally graded composite nanoshells in the presence of modal interaction. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(5), 237 (2020)

    Article  Google Scholar 

  24. LI, H., LV, H., SUN, H., QIN, Z., XIONG, J., HAN, Q., LIU, J., and WANG, X. Nonlinear vibrations of fiber-reinforced composite cylindrical shells with bolt loosening boundary conditions. Journal of Sound and Vibration, 496(31), 115935 (2021)

    Article  Google Scholar 

  25. YANG, Y., SAHMANI, S., and SAFAEI, B. Couple stress-based nonlinear primary resonant dynamics of FGM composite truncated conical microshells integrated with magnetostrictive layers. Applied Mathematics and Mechanics (English Edition), 42(2), 209–222 (2021) https://doi.org/10.1007/s10483-021-2704-6

    Article  MathSciNet  Google Scholar 

  26. WANG, X., ZHOU, G., SAFAEI, B., and SAHMANI, S. Boundary layer modeling of surface residual tension in postbuckling behavior of axially loaded silicon panels at nanoscale embedded in elastic foundations. Mechanics Based Design of Structures and Machines, 1–18 (2020) https://doi.org/10.1080/15397734.2020.1794889

  27. LIU, J. C., ZHANG, Y. Q., and FAN, L. F. Nonlocal vibration and biaxial buckling of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between. Physics Letters, Section A: General, Atomic and Solid State Physics, 381(14), 1228–1235 (2017)

    Article  MathSciNet  Google Scholar 

  28. JOSHI, P. V., GUPTA, A., JAIN, N. K., SALHOTRA, R., RAWANI, A. M., and RAMTEKKAR, G. D. Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non classical Kirchhoff’s plate theory: an analytical approach. International Journal of Mechanical Sciences, 131–132, 155–170 (2017)

    Article  Google Scholar 

  29. RADIĆ, N. and JEREMIĆ, D. A comprehensive study on vibration and buckling of orthotropic double-layered graphene sheets under hygrothermal loading with different boundary conditions. Composites Part B: Engineering, 128, 182–199 (2017)

    Article  Google Scholar 

  30. AL-SHUJAIRI, M. and MOLLAMAHMUTOǦLU, Ç. Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect. Composites Part B: Engineering, 154, 292–312 (2018)

    Article  Google Scholar 

  31. JAMALPOOR, A., AHMADI-SAVADKOOHI, A., HOSSEINI, M., and HOSSEINI-HASHEMI, S. Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco- Pasternak medium via nonlocal elasticity theory. European Journal of Mechanics, A/Solids, 63, 84–98 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  32. HAJMOHAMMAD, M. H., ZAREI, M. S., SEPEHR, M., and ABTAHI, N. Bending and buckling analysis of functionally graded annular microplate integrated with piezoelectric layers based on layerwise theory using DQM. Aerospace Science and Technology, 79, 679–688 (2018)

    Article  Google Scholar 

  33. LU, L., GUO, X., and ZHAO, J. On the mechanics of Kirchhoff and Mindlin plates incorporating surface energy. International Journal of Engineering Science, 124, 24–40 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  34. SARAFRAZ, A., SAHMANI, S., and AGHDAM, M. M. Nonlinear secondary resonance of nanobeams under subharmonic and superharmonic excitations including surface free energy effects. Applied Mathematical Modelling, 66, 195–226 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  35. SOBHY, M. and ZENKOUR, A. M. Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory. Composite Structures, 220, 289–303 (2019)

    Article  Google Scholar 

  36. LU, L., ZHU, L., GUO, X., ZHAO, J., and LIU, G. A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells. Applied Mathematics and Mechanics (English Edition), 40(12), 1695–1722 (2019) https://doi.org/10.1007/s10483-019-2549-7

    Article  MATH  Google Scholar 

  37. LU, L., GUO, X., and ZHAO, J. A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects. Applied Mathematical Modelling, 68, 583–602 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  38. FANG, J., ZHENG, S., XIAO, J., and ZHANG, X. Vibration and thermal buckling analysis of rotating nonlocal functionally graded nanobeams in thermal environment. Aerospace Science and Technology, 106, 106146 (2020)

    Article  Google Scholar 

  39. PHUNG-VAN, P., THAI, C. H., NGUYEN-XUAN, H., and ABDEL-WAHAB, M. An isogeometric approach of static and free vibration analyses for porous FG nanoplates. European Journal of Mechanics, A/Solids, 78, 103851 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  40. LIM, C. W., ZHANG, G., and REDDY, J. N. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. Journal of the Mechanics and Physics of Solids, 78, 298–313 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  41. ERINGEN, A. C. Linear theory of nonlocal elasticity and dispersion of plane waves. International Journal of Engineering Science, 10(5), 425–435 (1972)

    Article  MATH  Google Scholar 

  42. FAN, F., SAFAEI, B., and SAHMANI, S. Buckling and postbuckling response of nonlocal strain gradient porous functionally graded micro/nano-plates via NURBS-based isogeometric analysis. Thin-Walled Structures, 159, 107231 (2021)

    Article  Google Scholar 

  43. FAN, F., SAHMANI, S., and SAFAEI, B. Isogeometric nonlinear oscillations of nonlocal strain gradient PFGM micro/nano-plates via NURBS-based formulation. Composite Structures, 255, 112969 (2021)

    Article  Google Scholar 

  44. SHEN, H. S. Thermal postbuckling of shear deformable FGM cylindrical shells with temperature-dependent properties. Mechanics of Advanced Materials and Structures, 14(6), 439–452 (2007)

    Article  Google Scholar 

  45. MILLER, R. E. and SHENOY, V. B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11(3), 139–147 (2000)

    Article  Google Scholar 

  46. ZHAO, X., LEE, Y. Y., and LIEW, K. M. Mechanical and thermal buckling analysis of functionally graded plates. Composite Structures, 90(2), 161–171 (2009)

    Article  Google Scholar 

  47. ZHANG, L. W., ZHU, P., and LIEW, K. M. Thermal buckling of functionally graded plates using a local Kriging meshless method. Composite Structures, 108(1), 472–492 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil and Architecture Engineering, Nanchang Institute of Technology, Nanchang, 330099, China

    Rui Song

  2. Mechanical Rotating Equipment Department, Niroo Research Institute (NRI), Tehran, 14665-517, Iran

    S. Sahmani

  3. Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, 99628, North Cyprus via Mersin 10, Turkey

    B. Safaei

Authors
  1. Rui Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Sahmani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Safaei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Safaei.

Additional information

Project supported by the Natural Science Foundation of Jiangxi Science and Technology Department (No. 20202BAB204027)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Song, R., Sahmani, S. & Safaei, B. Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes. Appl. Math. Mech.-Engl. Ed. 42, 771–786 (2021). https://doi.org/10.1007/s10483-021-2725-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-021-2725-7

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation