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Static analysis of point-supported super-elliptical plates

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Abstract

This paper reports the static analysis of point-supported super-elliptical plates of uniform thickness subjected to a uniformly distributed lateral load. The plate perimeter was defined by a super-elliptic function with a power, corresponding to shapes ranging from an ellipse to a rectangle. The analysis was based on the Kirchhoff–Love plate theory and the computations were carried out by the Ritz method. Lagrange multipliers were used to satisfy the boundary conditions. Isotropic and homogeneous plates with 20 different shapes were examined for two distinct aspect ratios. Convergence studies were performed for the central deflection and the central bending moments. The results were checked against those of a corner-supported square plate and good agreement was obtained.

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References

  1. Altekin, M.: Static and Dynamic Analysis of Super-elliptical Plates. Ph.D. Thesis. Bogazici University, Istanbul (2005)

  2. Bathe K.J. (1996). Finite Element Procedures. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  3. Bayer I., Güven U. and Altay G. (2002). A parametric study on vibrating clamped elliptical plate with variable thickness. J. Sound Vib. 254(1): 179–188

    Article  Google Scholar 

  4. Chakraverty S., Bhat R.B. and Stiharu I. (1999). Recent research on vibration of structures using boundary characteristic orthogonal polynomials in the Rayleigh–Ritz method. Shock Vib. Dig. 31(3): 187–194

    Article  Google Scholar 

  5. Chakraverty S., Bhat R.B. and Stiharu I. (2001). Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh–Ritz method. J. Sound Vib. 241(3): 524–539

    Article  Google Scholar 

  6. Chen C.C., Lim C.W., Kitipornchai S. and Liew K.M. (1999). Vibration of symmetrically laminated thick super elliptical plates. J. Sound Vib. 220(4): 659–682

    Article  Google Scholar 

  7. Eschenauer H., Olhoff N. and Schnell W. (1997). Applied Structural Mechanics. Springer, Berlin

    Google Scholar 

  8. Gorman D.J. (1980). Free vibration analysis of rectangular plates with symmetrically distributed point supports along the edges. J. Sound Vib. 73(4): 563–574

    Article  MATH  MathSciNet  Google Scholar 

  9. Kerstens J.G.M. (1979). Vibration of a rectangular plate supported at an arbitrary number of points. J. Sound Vib. 65(4): 493–504

    Article  MATH  MathSciNet  Google Scholar 

  10. Kim C.S. (2003). Natural frequencies of orthotropic, elliptical and circular plates. J. Sound Vib. 259(3): 733–745

    Article  Google Scholar 

  11. Lee L.T. and Lee D.C. (1997). Free vibration of rectangular plates on elastic point supports with the application of a new type of admissible function. Comput. Struct. 65(2): 149–156

    Article  MATH  Google Scholar 

  12. Lee S.L. and Ballesteros P. (1960). Uniformly loaded rectangular plate supported at the corners. Int. J. Mech. Sci. 2: 206–211

    Article  Google Scholar 

  13. Leissa A.W. and Shihada S. (1995). Convergence of the Ritz method. Appl. Mech. Rev. 48(11): 90–95

    Article  Google Scholar 

  14. Liew K.M. and Feng Z.C. (2001). Three-dimensional free vibration analysis of perforated superelliptical plates via the p-Ritz method. Int. J. Mech. Sci. 43: 2613–2630

    Article  Google Scholar 

  15. Liew K.M., Kitipornchai S. and Lim C.W. (1998). Free vibration analysis of thick superelliptical plates. J. Eng. Mech. 124(2): 137–145

    Article  Google Scholar 

  16. Liew K.M. and Wang C.M. (1992). Vibration analysis of plates by the pb-2 Rayleigh–Ritz method: mixed boundary conditions, reentrant corners and internal curved supports. Mech. Struct. Mach. 20(3): 281–292

    Article  Google Scholar 

  17. Maron M.J. and Lopez R.J. (1991). Numerical Analysis: A Practical Approach. Wadsworth, California

    MATH  Google Scholar 

  18. McFarland D., Smith B.L. and Bernhart W.D. (1972). Analysis of Plates. Spartan, New York

    Google Scholar 

  19. Pan H.H. (1961). Note on “The uniformly loaded rectangular plate supported at the corners”. Int. J. Mech. Sci. 2: 313–315

    Article  Google Scholar 

  20. Rajalingham C., Bhat R.B. and Xistris G.D. (1995). A note on elliptical plate vibration modes as a bifurcation from circular plate modes. Int. J. Mech. Sci. 37(1): 61–75

    Article  MATH  Google Scholar 

  21. Szilard R. (1974). Theory and Analysis of Plates. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  22. Timoshenko S. and Woinowsky-Krieger S. (1959). Theory of Plates and Shells. McGraw-Hill, New York

    Google Scholar 

  23. Venkateshwar R., Rao B.N. and Prasad K.L. (1992). Stability of simply supported and clamped elliptical plates. J. Sound Vib. 159(2): 378–381

    Article  MATH  Google Scholar 

  24. Wang C.M. and Liew K.M. (1993). Buckling of elliptic plates under uniform pressure. J. Struct. Eng. ASCE 119(11): 3418–3425

    Article  Google Scholar 

  25. Wang C.M., Wang L. and Liew K.M. (1994). Vibration and buckling of super elliptical plates. J. Sound Vib. 171(3): 301–314

    Article  MATH  Google Scholar 

  26. Wang C.M., Wang Y.C. and Reddy J.N. (2002). Problems and remedy for the Ritz method in determining stress resultants of corner supported rectangular plates. Comput. Struct. 80: 145–154

    Article  Google Scholar 

  27. Zhong H., Li X. and He Y. (2005). Static flexural analysis of elliptic Reissner–Mindlin plates on a Pasternak foundation by the triangular differential quadrature method. Arch. Appl. Mech. 74: 679–691

    Article  MATH  Google Scholar 

  28. Zhou D., Lo S.H., Cheung Y.K. and Au F.T.K. (2004). 3D vibration analysis of generalized super elliptical plates using Chebyshev–Ritz method. J. Solids Struct. 41: 4697–4712

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Yildiz Technical University, 34349, Besiktas, Istanbul, Turkey

    M. Altekin

  2. Department of Civil Engineering, Bogazici University, 34342, Bebek, Istanbul, Turkey

    G. Altay

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  1. M. Altekin
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  2. G. Altay
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Correspondence to M. Altekin.

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Altekin, M., Altay, G. Static analysis of point-supported super-elliptical plates. Arch Appl Mech 78, 259–266 (2008). https://doi.org/10.1007/s00419-007-0154-9

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  • DOI: https://doi.org/10.1007/s00419-007-0154-9

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