A study of the stable equilibrium of thin shells compliant to shear and compression

Using relations of the geometrically nonlinear theory of thin shells compliant to shear and compression (the six-modal variant), we have written the key equations for determining their initial post-critical state by the finite element method. A specific feature of this model lies in the semidiscretization of the vector of displacements of an elastic body with respect to its variable thickness, based on the Timoshenko–Mindlin kinematic hypotheses, with preservation of the total vector of rotations of a normal to the median surface. We have solved numerically the problem of the stability of a circular plate, clamped over its contour, under the action of radial compressive forces, distributed uniformly along the contour. We have also performed a comparative analysis of the numerical solutions obtained and data known from the literature.

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Correspondence to I. E. Bernakevych.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 53, No. 4, pp. 162–168, October–December, 2010.

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Bernakevych, I.E., Vahin, P.P. & Shot, I.Y. A study of the stable equilibrium of thin shells compliant to shear and compression. J Math Sci 181, 497–505 (2012). https://doi.org/10.1007/s10958-012-0701-y

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Keywords

  • Circular Plate
  • Thin Shell
  • Nonlinear Theory
  • Median Surface
  • Total Potential Energy