TECHNICAL PAPERS
Nov 1, 1992

Axisymmetric General Shells and Jointed Shells of Revolution

Publication: Journal of Structural Engineering
Volume 118, Issue 11

Abstract

An iterative numerical method is presented for the analysis of axisymmetric, isotropic general shells with varying wall rigidity. Shell elements of special geometric shapes, e.g., cylindrical, spherical, and conical shells, are also considered. One‐dimensional finite difference points are used to discretize the shell elements into strips along the meridian. An iterative technique is then employed to determine the displacements and stresses. The solution to jointed shells is determined by the well‐known stiffness approach. The proposed method is applicable to any variation in rigidity along the meridian and to general axisymmetric loading conditions.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Au, T., Goodman, L. E., and Newmark, N. M. (1951), “A numerical procedure for the analysis of pressure vessel heads.” Technical Report, Department of Civil Engineering, University of Illinois, Urbana, Ill.
2.
Barony, S. Y., and Tottenham, H. (1976). “The analysis of rotational shells using a curved ring element and the mixed variational formulation.” Int. J. Numer. Methods in Engrg., 10, 861–872.
3.
Billington, D. P. (1971). “Concrete thin shells of revolution.” Concrete thin shells, Special Publication SP‐28, American Concrete Institute, Detroit, Mich., 237–274.
4.
Billington, D. P. (1982). Thin shell concrete structures. 2nd Ed., McGraw‐Hill, New York, N.Y.
5.
Brøndum‐Nielsen, T. (1962). “Axisymmetric bending of shells,” thesis presented to the Technical University of Denmark, at Copenhagen, Denmark, in partial fulfillment of the requirements for the degree of Doctor of Science.
6.
Budiansky, B., and Radkowski, P. P. (1963). “Numerical analysis of asymmetrical bending of shells of revolution.” Am. Inst. Aeronaut. Astronaut. J., 1(8), 1833–1842.
7.
Delpak, R. (1980). “Static analysis of thin rotational shells.” Comput. Struct., 11(4), 305–325.
8.
Elias, Z. M. (1972). “Mixed finite element method for axisymmetric shells.” Int. J. Numer. Methods Engrg., 4, 261–277.
9.
Flüge, W. (1960). Stresses in shells. Springer‐Verlag, Berlin, Germany.
10.
Geckeler, J. W. (1926). “Über die festigkeit Aahsensymetrischer schalen.” Forschugsarb Ingwes., Berlin, Germany, 276, 1–52 (in German).
11.
Ghali, A., and Neville, A. M. (1989). Structural analysis: A unified classical and matrix approach. 3d Ed., Chapman and Hall, New York, N.Y.
12.
Grafton, P. E., and Strome, D. R. (1963). “Analysis of axisymmetrical shells by direct stiffness method.” Am. Inst. Aeronaut. Astronaut. J., 1(10), 2342–2347.
13.
Horvay, G., Linkous, C., and Born, J. S. (1956). “Analysis of short thin shells under axisymmetrical edge loading.” J. Appl. Mech., ASME, 23 (March), 68–72.
14.
Jianping, P., and Harik, I. E. (1990). “Iterative FD solution to bending of axisymmetric conical shells.” J. Struct. Engrg., ASCE, 116(9), 2433–2447.
15.
Jianping, P., and Harik, I. E. (1991). “Axisymmetric pressures and thermal gradients in conical missile tips.” J. Aerosp. Engrg., ASCE, 4(3), 237–255.
16.
Jones, R. E., and Strome, D. R. (1966). “Direct stiffness method of analysis of shells of revolution utilizing curved elements.” Am. Inst. Aeronaut. Astronaut. J., 4(9), 1519–1525.
17.
Kelkar, V. S., and Sewell, R. T. (1987). Fundamentals of the analysis and design of shell structures. Prentice‐Hall, Inc., Englewood Cliffs, N.J.
18.
Kraus, H. (1967). Thin elastic shells. John Wiley and Sons, Inc., New York, N.Y.
19.
Kohnke, P. C. (1989). ANSYS engineering analysis system—Theoretical manual. Swanson Analysis Systems, Inc., Houston, Pa.
20.
Meissner, E. (1925). “Zur festigkeitsberechnung von hochdruckkesseltrommeln.” Schweizerische Bauzeitung, 86, 1–25 (in German).
21.
Meyer, R. R., and Harmon, M. B. (1963). “Conical segment method for analyzing open crown shells of revolution for edge leading.” Am. Inst. Aeronaut. Astronaut. J., 1(4), 886–891.
22.
Oñate, E., and Suarez, B. (1983). “A unified approach for the analysis of bridges, plates and axisymmetric shells using the linear Mindlin strip element.” Comput. Struct., 17(3), 407–426.
23.
Panda, S. C., and Natarajan, R. (1976). “Finite element analysis of laminated shells of revolution.” Comput. Struct., 6, 61–64.
24.
Parme, A. (1950). “Solution of difficult structural problems by finite differences.” J. Am. Concr. Inst., 47(3), 237–256.
25.
Pasternak, P. (1926). “HAUPTAUFSÄTZE die praktische berechnung biegefester kugelschalen, kreisrunder fundamentplatten auf elastischer bettung und kreiszylindrischer wandungen in gegenseitiger monolither verbindung.” Zeitschrift fur Angewandte Mathematik und Mechanik, 6, 1–29 (in German).
26.
Percy, J. H., Pian, T. H. H., Klein, S., and Navaratna, D. R. (1965). “Application of matrix displacement method to linear elastic analysis of shells of revolution.” Am. Inst. Aeronaut. Astronaut. J., 3(11), 2138–2145.
27.
Radkowski, P. P., Davis, R. M., and Bolduc, M. R. (1962). “Numerical analysis of equations of thin shells of revolution.” Am. Rocket Soc., 32, 36–41.
28.
Schnobrich, W. C. (1987). “Different methods of numerical analysis of shells.” Bull. Int. Assoc. Shell Spatial Struct., XXVII‐2(94), 55–63.
29.
Sepetoski, W. K., Pearson, C. E., Dingwell, I. W., and Adkins, A. W. (1962). “A digital program for the general axially symmetric thin‐shell problem.” J. Appl. Mech., ASME, 84 (December), 655–661.
30.
Spotts, M. F. (1939). “Analysis of spherical shells of variable wall thickness.” J. Appl. Mech., ASME, 61, A‐97–A‐102.
31.
Timoshenko, S., and Woinowsky‐Krieger, S. (1959). Theory of plates and shells. McGraw‐Hill, New York, N.Y.
32.
Watts, G. W., and Burrows, W. R. (1969). “The basic elastic theory of vessel heads under internal pressure.” J. Appl. Mech., ASME, 71 (March), 55–73.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 118Issue 11November 1992
Pages: 3186 - 3202

History

Published online: Nov 1, 1992
Published in print: Nov 1992

Permissions

Request permissions for this article.

Authors

Affiliations

Pei Jianping
Sr. Design Engr., Ningxia Arch. Design Inst., Yinchuan, People's Republic of China; currently, Visiting Scholar, Dept. of Civ. Engrg., Univ. of Kentucky, Lexington, KY 40506‐0046
Issam E. Harik, Member, ASCE
Assoc. Prof., Dept. of Civ. Engrg., Univ. of Kentucky, Lexington, KY

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share