Large deflection analysis of point supported super-elliptical plates


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Altekin M.

Structural Engineering and Mechanics, vol.51, no.2, pp.333-347, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.12989/sem.2014.51.2.333
  • Title of Journal : Structural Engineering and Mechanics
  • Page Numbers: pp.333-347
  • Keywords: super-elliptical, plate, nonlinear, bending, large deflection, FREE-VIBRATION ANALYSIS, LAMINATED COMPOSITE PLATES, NONLINEAR BENDING ANALYSIS, FINITE-ELEMENT-ANALYSIS, CIRCULAR PLATES, THIN PLATES, RITZ METHOD, SUPERELLIPTICAL PLATES, COLLOCATION SOLUTION, VARIABLE-THICKNESS

Abstract

Nonlinear bending of super-elliptical plates of uniform thickness under uniform transverse pressure was investigated by the Ritz method. The material was assumed to be homogeneous and isotropic. The contribution of the boundary conditions at the point supports was introduced by the Lagrange multipliers. The solution was obtained by the Newton-Raphson method. The influence of the location of the point supports on the central deflection was highlighted by sensitivity analysis. An approximate relationship between the central deflection and the super-elliptical power was obtained using the method of least squares. The critical points where the maximum deflection may develop, and the influence of nonlinearity were highlighted. The nonlinearity was found to be sensitive to the aspect ratio. The accuracy of the algorithm was validated by comparing the central deflection with the solutions of elliptical and rectangular plates.