Using RBF-FD for calculation of hydroelastic vibrations of axisymmetric orthotropic shells of rotation

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Abstract

Geometrically nonlinear differential equations describing the dynamic deformation of axisymmetric shells of rotation are derived on the basis of general equations for solving functions in the global coordinate system. The equations take into account thinning/thickening at large longitudinal strains as well as transverse shear for thick shells. The motion and pressure of an ideal incompressible fluid is described by a displacement potential. To obtain the numerical solution, the finite difference method based on spline interpolation by polyharmonic radial basis functions is applied. The calculation method is implemented in software package. Good agreement of the calculated displacements with the results of modeling by different finite elements in ANSYS is obtained. The frequencies of the hydroelastic vibrations of the tanks are compared with those obtained by the finite element and boundary element method, as well as with results from published articles by other researchers.

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About the authors

С. M. Nguyen

Novosibirsk State Technical University

Author for correspondence.
Email: mckq1985@gmail.com
Russian Federation, Novosibirsk

D. R. Shelevaya

Novosibirsk State Technical University; Lavrentyev Institute of Hydrodynamics of the Siberian Branch of the Russian Academy of Sciences

Email: mckq1985@gmail.com
Russian Federation, Novosibirsk; Novosibirsk

D. А. Krasnorutsky

Novosibirsk State Technical University; S.A. Chaplygin Siberian Research Institite of Aviation

Email: mckq1985@gmail.com
Russian Federation, Novosibirsk; Novosibirsk

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Supplementary files

Supplementary Files
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2. Fig. 1. Deformation and equilibrium of a small shell element.

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3. Fig. 2. Axisymmetric shell of revolution with liquid.

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4. Fig. 3. Examples of filling the calculation area with nodes.

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5. Fig. 4. Cylindrical shell. Calculation results.

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6. Fig. 5. Clamped cylindrical shell. Calculation results.

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7. Fig. 6. Elliptical shell. Calculation results.

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8. Fig. 7. Cylindrical (a) and elliptical (b) shells, dependence of displacement on pressure.

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9. Fig. 8. Conical shell. Calculation results.

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10. Fig. 9. Composite shell. Calculation results.

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11. Fig. 10. Conical (a) and composite (b) shells, dependence of displacement on pressure.

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12. Fig. 11. Convergence of frequencies of hydroelastic oscillations of a hemispherical shell with water.

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13. Fig. 12. Forms of oscillations of a toroidal tank (FEM-MGE [4] (a), DARSYS (b), frequency convergence (c)).

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Note

Presented by Academician of the RAS B.D. Annin


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