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Dynamic and static loss in stability of flexible spherical shells made out of a composite material

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Abstract

The dynamic and static stability of shallow spherical shells which are rectangular in a plane are investigated. It is assumed that the shell is made out of a composite material which is weakly shear resistant and hence the refined theories which allow for transverse shear deformations and rotational inertia are applied. The solutions which were obtained are compared with solutions founded on the basis of the Kirchhoff-Love theory. It is shown that the results which are obtained on the basis of the classical theory are high for both the static and dynamic loss in stability, and are qualitatively different from the results obtained using the refined theory. The solutions were obtained using the Bubnov-Galerkin method in the higher approximations.

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Literature cited

  1. M. P. Sheremet'ev and B. L. Pelekh, “On the question of the variation principle in the theory of shells”, in: Theoretical and Applied Mathematics [in Russian], No. 2, L'vov (1964), p. 45.

  2. V. A. Krys'ko and A. N. Kutsemako, “Investigation of the nonlinear vibrations of rectangular disks allowing for rotational inertia on the basis of several kinematic models”, in: Differential Equations and Calculus [in Russian], No. 4, Saratov (1974), pp. 129–143.

  3. A. S. Vol'mir, The Nonlinear Dynamics of Disks and Shells [in Russian], Moscow (1972).

  4. V. V. Amel'chenko, E. F. Burmistrov, and V. A. Krys'ko, “On the numerical investigation of the convergence of the Kantorovich-Vlasov method for flexible shells”, Prikl. Mekh.,9, No. 12, 15–21 (1973).

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Authors
  1. V. A. Krys'ko
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  2. A. N. Kutsemako
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Additional information

Saratovsk Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1108–1111, November–December, 1975.

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Krys'ko, V.A., Kutsemako, A.N. Dynamic and static loss in stability of flexible spherical shells made out of a composite material. Polymer Mechanics 11, 950–952 (1975). https://doi.org/10.1007/BF00857625

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  • DOI: https://doi.org/10.1007/BF00857625

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