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Static analysis of thin-walled beams using two-phase local-nonlocal integral model

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Języki publikacji
EN
Abstrakty
EN
A mathematical model is developed for static analysis of small-scale thinwalled beams having arbitrary cross sections. Constitutive relations of the thin-walled beams are defined upon the two-phase local-nonlocal mixture model with integral formulation. The developed model includes flexural-torsional coupling and warping effects. Governing equations of the thin-walled beams having nonlocal property are derived by using the principle of minimum potential energy. The displacement based finite element method is used to solve both local and nonlocal part of the model. The effect of the nonlocal parameters on the static behavior of micro-scale thin-walled beams having closed and open cross-sections is examined and discussed for various nonlocal parameters and boundary conditions.
Rocznik
Strony
673--695
Opis fizyczny
Bibliogr. 31 poz., rys., tab., wykr.
Twórcy
autor
  • Isparta Applied Sciences University, Technology Faculty, Mechanical Engineering Department, Isparta, Turkey
Bibliografia
  • 1. S.P. Timoshenko, J.N. Goodier, Theory of Elasticity, McGraw-Hill, New York, 1951.
  • 2. V.Z. Vlasov, Thin-Walled Elastic Beams, National Technical Information Service,Washington DC, 1961.
  • 3. A. Gjelsvik, The Theory of Thin-Walled Bars, Wiley, New York, 1981.
  • 4. L.S. Librescu, Thin-walled Composite Beams: Theory and Application, Springer, Netherlands, 2005.
  • 5. A.C. Eringen, Theory of nonlocal elasticity and some applications, Res Mechanica, 21, 4, 313–342, 1987.
  • 6. N.A. Fleck, J.W. Hutchinson, A phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids, 41, 12, 1825–1857, 1993.
  • 7. H. Neuber, On the general solution of linear-elastic problems in isotropic and anisotropic Cosserat continua, in: Applied Mechanics, pp. 153–158, Springer, Berlin, 1966.
  • 8. M.E. Gurtin, A.I. Murdoch, Surface stress in solids, International Journal of Solids and Structures, 14, 6, 431–440, 1978.
  • 9. J. Peddieson, G.R. Buchanan, R.P. Mcnitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 3-5, 305–312, 2003.
  • 10. N. Challamel, C. Wang, The small length scale effect for a non-local cantilever beam: a paradox solved, Nanotechnology, 19, 34, 345703, 2008.
  • 11. G. Romano, R. Barretta, M. Diaco, F.M. de Sciarra, Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, International Journal of Mechanical Sciences, 121, 151–156, 2017.
  • 12. C. Li, L.Q. Yao, W.Q. Chen, S. Li, Comments on nonlocal effects in nano-cantilever beams, International Journal of Engineering Science, 87, 47–57, 2015.
  • 13. R. Barretta, F.M. De Sciarra, Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams, International Journal of Engineering Science, 130, 187–198, 2018.
  • 14. C. Polizzotto, Nonlocal elasticity and related variational principles, International Journal of Solids and Structures, 38, 42–43, 7359–7380, 2001.
  • 15. N. Challamel, C. Wang, I. Elishakoff, Discrete systems behave as nonlocal structural elements: bending, buckling and vibration analysis, European Journal of Mechanics-A/Solids, 44, 125–135, 2014.
  • 16. M.F. Oskouie, R. Ansari, H. Rouhi, Bending of Euler–Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach, Acta Mechanica Sinica, 34, 871–882, 2018.
  • 17. G. Romano, R. Barretta, Nonlocal elasticity in nanobeams: the stress-driven integral model, International Journal of Engineering Science, 115, 14–27, 2017.
  • 18. F.P. Pinnola, M.S. Vaccaro, R. Barretta, F.M. De Sciarra, Random vibrations of stress-driven nonlocal beams with external damping, Meccanica, 56, 1329–1344, 2021.
  • 19. F.P. Pinnola, M.S. Vaccaro, R. Barretta, F.M. De Sciarra, Finite element method for stress-driven nonlocal beams, Engineering Analysis with Boundary Elements, 134, 22–34, 2022.
  • 20. A.A. Pisano, P. Fuschi, C. Polizzotto, Integral and differential approaches to Eringen’s nonlocal elasticity models accounting for boundary effects with applications to beams in bending, ZAMM-Journal of Applied Mathematics and Mechanics (Zeitschrift für Angewandte Mathematik und Mechanik), 101, 8, 202000152, 2021.
  • 21. N. Challamel, J. Reddy, C. Wang, Eringen’s stress gradient model for bending of nonlocal beams, Journal of Engineering Mechanics, 142, 12, 04016095, 2016.
  • 22. J. Fernandez-Saez, R. Zaera, J.A. Loya, J.N. Reddy, Bending of Euler–Bernoulli beams using Eringen’s integral formulation: a paradox resolved, International Journal of Engineering Science, 99, 107–116, 2016.
  • 23. A.D. Polyanin, A.V. Manzhirov, Handbook of Integral Equations, CRC Press, New York, 2008.
  • 24. H.C. Li, L.L. Ke, J. Yang, S. Kitipornchai, Size-dependent free vibration of microbeams submerged in fluid, International Journal of Structural Stability and Dynamics, 20, 12, 2020.
  • 25. M. Ghane, A.R. Saidi, R. Bahaadini, Vibration of fluid-conveying nanotubes subjected to magnetic field based on the thin-walled Timoshenko beam theory, Applied Mathematical Modelling, 80, 65–83, 2020.
  • 26. M. Soltani, F. Atoufi, F. Mohri, R. Dimitri, Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials, Thin-Walled Structures, 159, 2021.
  • 27. M.G. Günay, Buckling analysis of thin-walled beams by two-phase local–nonlocal integral model, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 47, 2, 765–777, 2023.
  • 28. M.G. Günay, Free vibration analysis of thin-walled beams using two-phase local–nonlocal constitutive model, Journal of Vibration and Acoustics, 145, 3, 031009, 2023.
  • 29. M.G. Günay, T. Timarci, Stresses in thin-walled composite laminated box-beams with curvilinear fibers: Antisymmetric and symmetric fiber paths, Thin-Walled Structures, 138, 170–182, 2019.
  • 30. M.G. Günay, T. Timarci, Static analysis of thin-walled laminated composite closedsection beams with variable stiffness, Composite Structures, 182, 67–78, 2017.
  • 31. J. Reddy, S. Pang, Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103, 2, 023511, 2008.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6b36cb4c-82e7-4b7a-96cb-cf4513363ba1
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