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A modified approach for the thermoelastic large deflection in the elliptical plate

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Abstract

The present paper deals with an investigation into the thermoelastic effect on the elliptical plate during large deflection while heating with non-stationary temperature distribution. The governing equation for the deflection is formulated with modification within the existing methodology devised by Berger. Thermally induced deflection results and its associated stresses are obtained in terms of Mathieu function of the first kind of order 2n. Furthermore, aforementioned problems can be degenerated into the problems of the circular region by applying limiting conditions. Some results which are derived by means of computational tools are illustrated numerically and depicted graphically.

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References

  1. Chia, C.Y.: Nonlinear Analysis of Plates. McGraw-Hill, New York (1980)

    Google Scholar 

  2. Sathyamoorthy, M.: Nonlinear Analysis of Structures. CRC Press, Boca Raton, FL (1998)

    MATH  Google Scholar 

  3. Wang, C.M., Lim, G.T.: Bending solutions of sectorial Mindlin plates from Kirchhoff plates. J. Eng. Mech. 126(4), 367–372 (2000)

    Article  Google Scholar 

  4. Altekin, M., Altay, G.: Static analysis of point-supported super-elliptical plates. Arch. Appl. Mech. 78(4), 259–266 (2008)

    Article  MATH  Google Scholar 

  5. Wang, C.Y.: Axisymmetrically supported heavy circular plate. Thin-Walled Struct. 42(12), 1709–1718 (2004)

    Article  Google Scholar 

  6. Altekin, M., Yukseler, R.F.: Large deflection analysis of clamped circular plates. In: Proceedings of The World Cong. on Eng., pp. 2210–2212 (2011)

  7. Nishawala, V.V.: A study of large deflection of beams and plates. Dissertation of Master Degree, New Brunswick: Rutgers University (2011)

  8. Davoodinik, A.R., Rahimi, G.H.: Large deflection of flexible tapered functionally graded beam. Acta Mech. 27, 767–777 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Golmakani, M.E., Kadkhodayan, M.: Large deflection thermoelastic analysis of functionally graded stiffened annular sector plates. Int. J. Mech. Sci. 69(1), 94–106 (2013)

    Article  Google Scholar 

  10. Golmakani, M.E., Emami, M.: Buckling and large deflection behaviors of radially functionally graded ring-stiffened circular plates with various boundary conditions. Appl. Math. Mech. 37(9), 1131–1152 (2016)

    Article  MathSciNet  Google Scholar 

  11. Eren, I.: Analyses of large deflections of simply supported nonlinear beams, for various arc length functions. Arab. J. Sci. Eng. 38(4), 947–952 (2013)

    Article  Google Scholar 

  12. Sitar, M., Kosel, F., Brojan, M.: A simple method for determining large deflection states of arbitrarily curved planar elastica. Arch. Appl. Mech. 84(2), 263–275 (2014)

    Article  MATH  Google Scholar 

  13. Jang, T.S.: A general method for analysing moderately large deflections of a non-uniform beam: an infinite Bernoulli-Euler-von Kármán beam on a nonlinear elastic foundation. Acta Mech. 225(7), 1967–1984 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yin, Z.: Large deflection of clamped circular plate and accuracy of its approximate analytical solutions. Sci. China Phys. Mech. Astro. 59(2), 1–11 (2016)

    Google Scholar 

  15. Choi, I.H.: Low-velocity impact response analysis of composite pressure vessel considering stiffness change due to cylinder stress. Compos. Struct. 160(15), 491–502 (2017)

    Article  Google Scholar 

  16. Berger, H.M.: A new approach to the analysis of large deflection of plates. ASME J. Appl. Mech. 22, 465–472 (1955)

    MathSciNet  MATH  Google Scholar 

  17. Tauchert, T.R.: Large plate deflections, Berger’s approximation. Encyclopedia of Thermal Stresses, Springer Reference, New York, pp. 5522–5537 (2014)

  18. Nowinski, J.L., Ohnabe, H.: On certain inconsistencies in Berger equations for large deflections of elastic plates. Int. J. Mech. Sci. 14, 165–170 (1972)

    Article  MATH  Google Scholar 

  19. Biswas, P.: Large deflection of a heated elliptical plate under stationary temperature. Def. Sci. J. 26, 41–46 (1976)

    MathSciNet  MATH  Google Scholar 

  20. Datta, S.: Large deflection of a heated elliptical plate on elastic foundation. Inst. J. Sci. 1, 185–197 (1976)

    MATH  Google Scholar 

  21. Ventsel, E., Krauthammer, T.: Thin Plates and Shells-Theory: Analysis and Applications. Marcel Dekker, New York (2001)

    Book  Google Scholar 

  22. Bhad, P.P., Varghese, V., Khalsa, L.H.: Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments. J. Therm. Stress. doi:10.1080/01495739.2016.1211496

  23. Wang, M.Z., Xu, X.S.: A generalization of Almansi’s theorem and its application. Appl. Math. Modelling 14, 275–279 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  24. McLachlan, N.W.: Theory and Application of Mathieu Function. Oxford University Press, Oxford (1947)

    MATH  Google Scholar 

  25. Bhad, P.P., Varghese, V.: Thermoelastic analysis on a circular plate subjected to annular heat supply. Gl. J. Res. Anal. 3(4), 141–145 (2014)

    Google Scholar 

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Acknowledgements

The author(s) are grateful to reviewer and editor for their valuable suggestion and constructive comments which resulted in revising the paper to its present form.

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Authors and Affiliations

  1. Priyadarshini J. L. College of Engg., Nagpur, India

    Pravin Bhad

  2. RTM Nagpur University, Nagpur, India

    Vinod Varghese

  3. M.G. College, Armori, Gadchiroli, India

    Lalsingh Khalsa

Authors
  1. Pravin Bhad
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  2. Vinod Varghese
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  3. Lalsingh Khalsa
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Correspondence to Pravin Bhad.

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Bhad, P., Varghese, V. & Khalsa, L. A modified approach for the thermoelastic large deflection in the elliptical plate. Arch Appl Mech 87, 767–781 (2017). https://doi.org/10.1007/s00419-016-1222-9

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