Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-19T13:16:17.026Z Has data issue: false hasContentIssue false

Analysis of shallow shells by a combination of finite elements and contour methods

Published online by Cambridge University Press:  17 February 2009

D. Bucco
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia, 5001.
J. Mazumdar
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia, 5001.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Two generalised shallow-shell bending elements are developed for the analysis of doubly-curved shallow shells having arbitrarily shaped plan-forms. Although both elements are formulated using the concept of iso-deflection contour lines, one element uses the three displacement components U, V and W as the basic unknowns, while the displacement component W and the stress function ф serve as the unknowns in the other element. A number of illustrative examples are included to demonstrate the accuracy and relative convergence of the proposed shallow-shell elements when employed for static analysis purposes.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1991

References

[1] Bhattacharya, B., “Analysis of shallow spherical shells in the form of an equilateral triangle in plan”, Proc. Instn. Civ. Engrs. 65 (2) (1978) 421429.Google Scholar
[2] Brebbria, C. A. and Nath, J. M. Deb, “A comparison of recent shallow shell finite element analysis”, Int. J. Mech. Sci. 12 (1970) 849857.CrossRefGoogle Scholar
[3] Broome, T. H. Jr and Hyman, B. I., “An analysis of shallow spheroidal shells by a semi-inverse contour method”, Int. J. Solids Struct. 11 (1975) 12811289.CrossRefGoogle Scholar
[4] Bucco, D., “A numerical procedure for the study of plates and shallow shells of arbitrary shape”, Ph.D. Thesis, Dept. Appl. Math., University of Adelaide, (1981).Google Scholar
[5] Bucco, D., Mazumdar, J. and Sved, G., “Application of the finite strip method combined with the deflection contour method to plate bending problems”, Comp. Struct. 10 (1978) 827830.CrossRefGoogle Scholar
[6] Clough, R. W. and Johnson, C. P., “A finite element approximation for the analysis of thin shells”, Int. J. Solids Struct. 4 (1968) 4360.CrossRefGoogle Scholar
[7] Connor, J. J. and Brebbria, C., “Stiffness matrix for shallow rectangular shell element”, Proc. ASCE, J. Engng. Mech. Div. 93 (1967) 4365.CrossRefGoogle Scholar
[8] Cowper, G. R., Lindberg, G. M. and Olson, M. D., “A shallow shell finite element of triangular shape”, Int. J. Solids. Struct. 6 (1970) 11331156.CrossRefGoogle Scholar
[9] Dawe, D. J., “High-order triangular finite elements for shell analysis”, Int. J. Solids. Struct. 11 (1975) 10971110.CrossRefGoogle Scholar
[10] Dhatt, G. S., “An efficient triangular shell element”, AIAA, Journal 8 (11) (1970) 21002102.CrossRefGoogle Scholar
[11] Greene, B. E., Jones, R. E., McLay, R. W. and Strome, D. R., “Dynamic analysis of shells using doubly-curved finite elements”, Proc. 2nd Conf. Matrix Methods Struct. Mech., Wright-Patterson Air Force Base, Ohio, (1968).Google Scholar
[12] Hutton, S. G. and Anderson, D. L., “Finite element method: a Galerkin approach”, Proc. ASCE, J. Engng. Mech. Div. 97 (1971) 15031520.CrossRefGoogle Scholar
[13] Jones, R., “Approximate methods for the linear and non-linear analysis of plates and shallow shells”, J. Struct. Mech. 5 (3) (1977) 233253.CrossRefGoogle Scholar
[14] Jones, R. and Mazumdar, J., “A method of static analysis of shallow shells”, AIAA, Journal 12 (8) (1974) 11341136.CrossRefGoogle Scholar
[15] Leissa, A. W. and Kadi, A. S., “Analysis of shallow shells by the method of point matching”, AFFDL, Wright Patterson Air Force Base, Ohio, Tech. Rep. AFFDL-TR-69–71, (1969).Google Scholar
[16] Mazumdar, J., “A method for solving problems of elastic plates of arbitrary shape”, J. Aust. Math Soc. 11 (1) (1970) 95112.CrossRefGoogle Scholar
[17] Olson, M. D. and Lindberg, G. M., “Dynamic analysis of shallow shells with a doubly-curved triangular finite element”, J. Sound Vib. 19 (3) (1971) 299318.CrossRefGoogle Scholar
[18] Pecknold, D. A. and Schnobrich, W. C., “Finite element analysis of skewed shallow shells”, Proc. ASCE, J. Struct. Div. 95 (1969) 715744.CrossRefGoogle Scholar
[19] Ramaswamy, G. S., “Design and construction of concrete shell roofs”, McGraw Hill, Inc. New Delhi, (1971).Google Scholar
[20] Sabir, A. B. and Ashwell, D. G., “A stiffness matrix for shallow shell finite elements”, Int. J. Mech. Sci. 11 (1969) 269279.CrossRefGoogle Scholar
[21] Strickland, G. E. and Loden, W. A., “A doubly-curved triangular shell element”, Proc. 2nd Conf. Matrix Methods Struct. Mech., Wright-Patterson Air Force Base, Ohio, (1968).Google Scholar
[22] Szabo, B. A. and Lee, G. C., “Stiffness matrix for plates by Galerkin's method”, Proc. ASCE J. Engng. Mech. Div. 95 (1969) 571585.CrossRefGoogle Scholar
[23] Vlasov, V. Z., “General theory of shells and its applications in engineering”, NASA TT. F-99, Washington, D. C, (1964).Google Scholar