Shell Elements for Cooling Tower Analysis
Publication: Journal of Engineering Mechanics
Volume 109, Issue 5
Abstract
Intending to achieve optimum finite element modeling of column supported cooling towers for seismic response studies according to the distributions of dominating bending and membrane stresses and intending to model the vulnerable shell‐column region using discrete column elements and quadrilateral shell elements, a set of elements is adopted, modified or extended. The set includes: (1) A 16 d.o.f. column element; (2) a 48 d.o.f. doubly curved quadrilateral general shell element; (3) a 42 d.o.f. doubly curved general‐membrane transition element; (4) a 21 d.o.f. and 39 d.o.f. doubly curved triangular membrane filler elements; and (5) a 28 d.o.f. doubly curved quadrilateral membrane element. Examples are given to evaluate a single type, combined types, and the whole set of elements with results in good agreement with alternative solutions. These elements may be used for accurate and efficient free vibration analysis of column supported cooling towers. The modeling may be used in seismic response analysis of cooling towers for obtaining detail stress distribution in the vulnerable shell‐column region. This model may be extended to include material nonlinearity in the shell‐column region for the seismic response studies.
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References
1.
Abu‐Sitta, S. H., and Davenport, A. G., “Earthquake Design of Cooling Towers,” Journal of the Structural Division, ASCE, Vol. 96, No. ST9, Proc. Paper 7524, Sept., 1970, pp. 1889–1902.
2.
Ashwell, D. G., and Gallagher, R. H., eds., Finite Elements for Thin Shells and Curved Members, John Wiley and Sons, Inc., New York, N.Y., 1976.
3.
Basu, P. K., and Gould, P. L., “Finite Element Discretization of Open‐Type Axisymmetric Elements,” International Journal for Numerical Methods in Engineering, Vol. 14, No. 2, 1979, pp. 159–178.
4.
Bogner, F. K., Fox, R. L., and Schmit, L. A., Jr., “A Cylindrical Shell Discrete Element,” American Institute of Aeronautics and Astronautics Journal, Vol. 5, No. 4, Apr., 1967, pp. 745–750.
5.
Carter, R. L., Robinson, A. R., and Schnobrich, W. C., “Free Vibration of Hyperbolidal Shells of Revolution,” Journal of the Engineering Mechanics Division, ASCE, Vol. 95, No. EM5, Proc. Paper 6808, Oct., 1969, pp. 1033–1052.
6.
Cowper, G. R., Lindberg, G. M., and Olson, M. D., “A Shallow Shell Finite Element of Triangular Shape,” International Journal of Solids and Structures, Vol. 6, 1970, pp. 1133–1156.
7.
Dawe, D. J., “High‐Order Triangular Finite Element for Shell Analysis,” International Journal of Solids and Structures, Vol. 6, 1975, pp. 1097–1110.
8.
Deb Nath, J. M., “Free Vibration, Stability and Nonclassical Modes of Cooling Tower Shells,” Journal of Sound and Vibration, Vol. 33, No. 1, 1974, pp. 79–101.
9.
Fonder, G. A., “Studies in Doubly Curved Elements for Shells of Revolution,” Finite Elements for Thin Shells and Curved Members, D. G. Ashwell and R. H. Gallagher, eds., John Wiley and Sons, Inc., New York, N.Y., 1976, pp. 113–129.
10.
Fonder, G. A., and Clough, R. W., “Explicit Addition of Rigid‐Body Motions in Curved Finite Elements,” American Institute of Aeronautics and Astronautics Journal, Vol. 11, No. 3, Mar., 1973, pp. 305–312.
11.
Gran, C. S., and Yang, T. Y., “Doubly Curved Membrane Shell Finite Element,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM4, Proc. Paper 14741, Aug., 1979, pp. 567–584.
12.
Gran, C. S., and Yang, T. Y., “NASTRAN AND SAP IV Applications on the Seismic Response of Column‐Supported Cooling Towers,” Journal of Computers and Structures, Vol. 8, No. 6, June, 1978, pp. 761–768.
13.
Gran, C. S., and Yang, T. Y., “Refined Analysis of the Seismic Response of Column Supported Cooling Towers,” Journal of Computers and Structures, Vol. 11, No. 3, 1980, pp. 225–231.
14.
Greene, B. E., Jones, R. E., McLay, R. W., and Strome, D. R., “Dynamic Analysis of Shells Using Doubly‐Curved Finite Elements,” Proceedings of the 2nd Conference on Matrix Methods in Structural Mechanics, Air Force Flight Dynamics Laboratory (TR‐68‐150), Dayton, Ohio, Dec., 1969, pp. 185–212.
15.
Gould, P. L., Sen, S. K., and Suryoutomo, H., “Dynamic Analysis of Column‐Supported Hyperboloidal Shells,” Earthquake Engineering and Structural Dynamics, Vol. 2, 1974, pp. 269–279.
16.
Hashish, M. G., and Abu‐Sitta, S. H., “Free Vibration of Hyperbolic Cooling Towers,” Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. EM2, Proc. Paper 8037, Apr., 1971, pp. 253–269.
17.
Kalnins, A., “Effect of Bending on Vibrations of Spherical Shells,” The Journal of the Acoustical Society of America, Vol. 36, No. 1, Jan., 1966, pp. 74–81.
18.
Larsen, P., “Large Displacement Analysis of Shells of Revolution Including Creep, Plasticity and Viscoelasticity,” thesis presented to the University of California at Berkeley, Calif., in 1972, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
19.
Miller, K. A. G., chairman, “Report of the Committee of Inquiry into the Collapse of the Cooling Tower at Ardeer Nylon Works, Ayrshire on Thursday, 27th September, 1973,” Imperial Chemical Industries Limited, Petrochemicals Division, available from Engineering Services Department, Imperial Chemical House, Millbank, London, England, SWIP 3JF, Mar., 1974.
20.
Nelson, R. L., “Free Vibration Analysis of Cooling Towers,” Shock and Vibration Digest, Vol. 12, No. 12, Dec., 1980, pp. 15–24.
21.
Novozhilov, V. V., Thin Shell Theory, 2nd ed., Wolters‐Noordhoff Publishing, Groningen, The Netherlands, 1970, pp. 22–23.
22.
“Report of the Committee of Inquiry into the Collapse of the Cooling Tower at Ferrybridge, Monday, Nov. 1, 1965,” Central Electricity Generating Board, Her Majesty's Stationary Office, London, England, 1966.
23.
Sen, S. K., and Gould, P. L., “Free Vibration of Shells of Revolution Using FEM,” Journal of the Engineering Mechanics Division, ASCE, Vol. 100, No. EM2, Proc. Paper 10488, Apr., 1974, pp. 283–303.
24.
Strang, G., and Fix, G. J., An Analysis of the Finite Element Method, Prentice‐Hall, Inc., Englewood Cliffs, N.J., 1973, pp. 156–163.
25.
Thomas, G. R., and Gallagher, R. H., “A Triangular Shell Finite Element: Linear Analysis,” C.R. 2482, National Aeronautics and Space Administration, Washington, D.C., July, 1975.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 109 • Issue 5 • October 1983
Pages: 1270 - 1289
Copyright
Copyright © 1983 ASCE.
History
Published online: Oct 1, 1983
Published in print: Oct 1983
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