**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31242

##### Axisymmetric Nonlinear Analysis of Point Supported Shallow Spherical Shells

**Authors:**
M. Altekin,
R. F. Yükseler

**Abstract:**

Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

**Keywords:**
Nonlinear,
Bending,
Plate,
Point support,
Shell

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1088844

**References:**

[1] N. Akkas, and R. Toroslu, “Snap-through buckling analyses of composite shallow spherical shells”, Mechanics of Composite Materials and Structures, vol. 6 (4), 1999, pp. 319-330.

[2] M. Altekin, and R. F. Yükseler, ”Axisymmetric large deflection analysis of an annular circular plate subject to rotational symmetric loading”, Proceedings of the Eleventh Int. Conference on Computational Structures Technology, Dubrovnik, September 2012.

[3] M. Altekin, and R. F. Yükseler, “Axisymmetric large deflection analysis of fully and partially loaded shallow spherical shells”, Structural Engineering and Mechanics, vol. 47 (4), 2013, pp. 559-573.

[4] R. A. Arciniega, and J. N. Reddy, “Large deformation analysis of functionally graded shells”, Int. J. of Solids and Structures, vol. 44 (6), 2007, pp. 2036-2052.

[5] D. H. Bich, D. V. Dung, and L. K. Hoa, “Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects”, Composite Structures, vol. 94 (9), 2012, pp. 2952-2960.

[6] N. D. Duc, and T. Q. Quan, “Nonlinear dynamic analysis of imperfect functionally graded material double curved thin shallow shells with temperature-dependent properties on elastic foundation”, J. of Vibration and Control, DOI: 10.1177/1077546313494114.

[7] N. C. Huang, “Unsymmetrical buckling of thin shallow spherical shells”, J. of Applied Mechanics, vol. 31 (3), 1964, pp. 447-457.

[8] V. A. Maksimyuk, E. A. Storozhuk, and I. S. Chernyshenko, “Using mesh-based methods to solve nonlinear problems of statics for thin shells”, Int. Applied Mechanics, vol. 45 (1), 2009, pp. 32-56.

[9] G. H. Nie, and J. C. Yao, “An asymptotic solution for non-linear behavior of ımperfect shallow spherical shells”, J. of Mechanics, vol. 26 (2), 2010, pp. 113-122.

[10] L. S. Ramachandra, and D. Roy, “A novel technique in the solution of axisymmetric large deflection analysis of a circular plate”, J. of Applied Mechanics, vol. 68 (5), 2001, pp. 814-816.

[11] K. Y. Sze, X. H. Liu, and S. H. Lo, “Popular benchmark problems for geometric nonlinear analysis of shells”, Finite Elements in Analysis and Design, vol. 40 (11), 2004, pp. 1551-1569.

[12] R. Szilard, Theory and Analysis of Plates. Englewood Cliffs, New Jersey: Prentice-Hall, 1974, pp 616-708.

[13] E. Ramm, and W. A. Wall, “Shell structures- a sensitive interrelation between physics and numerics", Int. J. for Numerical Methods in Engineering, vol. 60 (1), 2004, pp. 381-427.

[14] D. Chakravortya, J.N. Bandyopadhyaya, and P.K. Sinha, "Finite element free vibration analysis of point supported laminated composite cylindrical shells", J. of Sound and Vibration, vol. 181 (1), 1995, pp. 43–52.

[15] T. Irie, G. Yamada, and Y. Kudoh, "Free vibration of a point-supported circular cylindrical shell", J. of the Acoustical Society of America, vol. 75 (4), 1984, pp. 1118-1123.

[16] Y. Narita, and A. W. Leissa, "Vibrations of corner point supported shallow shells of rectangular planform", Earthquake Engineering & Structural Dynamics, vol. 12 (5), 1984, pp. 651-661.

[17] Y. Kobayashi, and A. W. Leissa, "Large amplitude free vibration of thick shallow shells supported by shear diaphragms", Int. J. of Non-Linear Mechanics, vol. 30 (1), 1995, pp. 57-66.