Cite this article as:
Bauer S. M., Voronkova E. B. On the Unsymmetrical Buckling of Shallow Spherical Shells under Internal Pressure. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2018, vol. 18, iss. 4, pp. 390-396. DOI: https://doi.org/10.18500/1816-9791-2018-18-4-390-396
On the Unsymmetrical Buckling of Shallow Spherical Shells under Internal Pressure
This work isdevoted to the numerical study of unsymmetrical buckling of shallow spherical shells and annular plates with varying mechanical characteristics subjected to internal pressure. We suppose that the edge of the shell is clamped but moving freely in the shell’s plane. For the annular plate a roller support is considered for the inner edge of the plate, i.e. the edge that can slide along the figure axes without changing the slope. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical methodise mployed to obtain the lowes tloadvalue which leads to the appearance of wavesin the circumferential direction. The effect of material inhomogeneity on the buckling load is examined. It is shown that if the elasticity modulus decreases away from the center of a plate, the critical pressure for unsymmetric buckling is sufficiently lower than for a plate with constant mechanical properties.
1. Panov D. Yu., Feodos’ev V. I. On the equilibrium and stability loss of shallow shells under large deflection. Prikl. Mat. Mekh. [J. Appl. Math. Mech.], 1948, vol. 12, iss. 4, pp. 389–406 (in Russian).
2. Feodos’ev V. I. On a method of solution of the nonlinear problems of stability of deformable systems. J. Appl. Math. Mech., 1963, vol. 27, iss. 2, pp. 392–404. DOI: https://doi.org/10.1016/0021-8928(63)90008-X
3. Morozov N. F. On the existence of a non-symmetric solution in the problem of large deflections of a circular plate with a symmetric load. Izv. Vyssh. Uchebn. Zaved. Mat., 1961, no. 2, pp. 126—129 (in Russian).
4. Piechocki W. J. On the non-linear theory of thin elastic spherical shells. Arch. Mech., 1969, no. 21, pp. 81–101.
5. Nai-Chien Huang. Unsymmetrical buckling of thin shallow spherical shells. J. Appl. Mech., 1964, no. 31, pp. 447—457. DOI: https://doi.org/10.1115/1.3629662
6. Cheo L. S., Reiss E. L. Unsymmetrical wrinkling of circular plates. Quart. Appl. Math., 1971, no. 31, pp. 75–91. DOI: https://doi.org/10.1090/qam/99710
7. Bauer S. M., Voronkova E. B. Models of shells and plates in the problems of ophthalmology. Vestnik St. Petersburg University: Mathematics, 2014, vol. 47, iss. 3, pp. 123–139. DOI: https://doi.org/10.3103/S1063454114030029
8. Bauer S. M., Voronkova E. B. On unsymmetrical buckling of circular plates under normal pressure. Vestnik St. Petersburg University. Ser. 1., 2012, iss. 1, pp. 80–85 (in Russian).
9. Coleman D. J., Trokel S. Direct-recorded intraocular pressure variations in a human subject. Arch Ophthalmol, 1969, vol. 82, no. 5, pp. 637—640. DOI: https://doi.org/10.1001/archopht.1969.00990020633011
10. Nesterov A. P. Basic principles of open angle glaucoma diagnostic. Vestnik of ophtalmology, 1998, no. 2, pp. 3–6 (in Russian).
