Archive of Applied Mechanics

, Volume 85, Issue 2, pp 287–302 | Cite as

The thermal bend of RTP with one edge clamped and two edges simply supported and one edge free

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Abstract

Small-deflection plate theory and superposition principle, with consideration of temperature variation that is perpendicular to the surface, reveal that a rectangular thin plate (RTP) with one edge clamped, two edges simply supported, and one edge free under temperature disparity can be regarded as a superposition of an RTP with three simply supported edges and one free edge under temperature disparity and an RTP with three simply supported edges and one free edge under bending moment on one edge. First, by supposing the deflection function that has undetermined parameters at the free edge and by adopting the Levy method, the closed solution for an RTP with three simply supported edges and one free edge is obtained. Second, the closed solution for an RTP with three simply supported edges and one free edge is obtained under temperature disparity. Third, with the use of the solution for an RTP with four simply supported edges under bending moment on one edge, the solution for an RTP with three simply supported edges and one free edge under bending moment on one edge is obtained. Finally, the deflection and bending analytical solution for an RTP with one edge clamped, two edges simply supported, and one edge free under temperature disparity is obtained by adopting the superposition principle. The calculation coefficient table for a concrete RTP with one edge clamped, two edges simply supported, and one edge free under temperature disparity is established by using MATLAB. Thus, a theoretical calculation based on a concrete RTP with one edge clamped, two edges simply supported, and one edge free under temperature disparity in an engineering structure is provided for engineering design.

Keywords

One edge clamped, two edges simply supported, and one edge free Rectangular thin plate Temperature Deflection Bending moment 
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References

  1. 1.
    Misra J.C.: On the thermal bending of a thin elastic simply supported rectangular plate resting on an elastic foundation. Pure Appl. Geophys. 112(1), 83–89 (1974)CrossRefGoogle Scholar
  2. 2.
    Pachinger F., Lrschik H.: Fast convergent series solutions for thermal bending of thin rectangular plates. J. Therm. Stress. 21(7), 763–775 (1998)CrossRefGoogle Scholar
  3. 3.
    Zhong Y., Zhang Y.S.: Theoretic solution for rectangular thin plate with arbitrary boundary conditions by symplectic geometry method. Chin. J. Appl. Mech. 22(2), 293–297 (2005)Google Scholar
  4. 4.
    Deshmukh K.C., Khandait M.V., Warbhe S.D. et al.: Thermal stresses in a simply supported plate with thermal bending moments. Appl. Math. Mech. 6(18), 1–12 (2010)Google Scholar
  5. 5.
    Cheng X.S., Du Y.F.: The discussion of the analytical solution about rectangular thin slab under temperature disparity with four simply supported edges. Low Temp. Archit. Technol. 4, 76–78 (2006)Google Scholar
  6. 6.
    Cheng X.S., Du Y.F., Li H.: Analytic solution to rectangular thin plate with three clamped edges and one simply supported edge under temperature disparity. Adv. Struct. Eng. 8, 789–794 (2006)Google Scholar
  7. 7.
    Cheng X.S., Du Y.F., Li H.: Discuss of analytic solution about rectangular thin plate with four clamped edges under temperature disparity. Spec. Struct. 23(4), 42–45 (2006)Google Scholar
  8. 8.
    Cheng X.S., Du Y.F., Li H.: A discussion on the analytical solution of rectangular thin slab under temperature load with four simply supported edges. Mech. Eng. 28(6), 28–32 (2006)Google Scholar
  9. 9.
    Cheng X.S., Du Y.F., Li H. et al.: Analytic solution about rectangular thin slab with three simply supported edges and one clamped edge under temperature load. Low Temp. Archit. Technol. 4, 59–61 (2007)Google Scholar
  10. 10.
    Cheng X.S., Du Y.F., Li H. et al.: The analytical solution about rectangular thin slab with three clamped edges and one simply supported edges under temperature load. Struct. Environ. Eng. 34(4), 8–13 (2007)Google Scholar
  11. 11.
    Cheng X.S., Du Y.F., Li H. et al.: The analytical solution about thin rectangular slab with two opposite clamped edges and two opposite simply supported edges under temperature loads. J. Gansu Sci. 19(2), 39–43 (2007)Google Scholar
  12. 12.
    Cheng X.S., Du Y.F., Li H.: An analytic solution for rectangular thin slab with two adjacent clamped edges and two adjacent simply supported edges under temperature loads. J. Gansu Sci. 20(1), 116–118 (2008)Google Scholar
  13. 13.
    Cheng X.S., Du Y.F., Li H., Su J.X.: The analytical Solution about rectangular thin slab with two opposite edges clamped and two opposite edges simply supported under temperature load. Proc. Tenth Int. Symp. Struct. Eng. Young Expert 10, 213–217 (2008)Google Scholar
  14. 14.
    Cheng X.S., Su J.X., Shi X.Y.: The thermal bend of concrete rectangular thin plate with four sides supported. Spec. Struct. 26(4), 56–60 (2009)Google Scholar
  15. 15.
    Liu J.X., Guo X.h., Su J.C.: Water Supply and Drainage Engineering Structure, pp. 295–344. China Construction Industry Press, Beijing (2006)Google Scholar
  16. 16.
    Cheng X.S., Du X.L.: The thermal bend of concrete rectangular thin plate with three clamped sides and one free side. Eng. Mech. 30(4), 97–106 (2013)MathSciNetGoogle Scholar
  17. 17.
    Cheng X.S., Du X.L., Zhang G.W. et al.: The thermal bend of concrete rectangular thin plate with three simply supported sides and one free side. Chin. J. Appl. Mech. 30(1), 37–42 (2013)Google Scholar
  18. 18.
    Fu B.L.: The Energy Principle and Its Application in Elastic Mechanics. Science Press, Beijing (2004)Google Scholar
  19. 19.
    Zhang F.F.: Elastic Thin Plate. Science Press, Beijing (1984)Google Scholar
  20. 20.
    Guo Z.H., Shi X.D.: Behaviour of Reinforced Concrete at Elevated Temperature and Its Calculation, pp. 106–108. Tsinghua University Press, Beijing (2003)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Civil EngineeringLanzhou University of TechnologyLanzhouChina

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