Algorithm for Aging Viscoelastic Structures Under Periodic Load
Publication: Journal of Engineering Mechanics
Volume 110, Issue 6
Abstract
A numerical step‐by‐step algorithm for the analysis of concrete structures exposed to a periodic history of environmental humidity or temperature is presented. The creep law of concrete is assumed to be linear, and the relationship between humidity and shrinkage is also linear. Cracking is assumed to be absent. The effect of concrete age on creep properties is taken into account. The creep law is considered in a rate‐type form corresponding to the Maxwell chain model. The well‐known exponential algorithm is generalized to complex variables to describe the periodic part of the response. Since this part cannot be separated in advance from the drifting mean response, the standard exponential algorithm in real variables and the new one in complex variables are used simultaneously in each time step to provide the total response. The algorithm allows an arbitrary increase of the time step, and time steps that are orders of magnitude larger than the fluctuation period, as well as the relaxation times, are possible without causing inaccuracies and numerical instability. The algorithm leads to a series of incremental elastic problems in which the stresses, strains, elastic moduli, stiffness matrices, etc., are all complex variables. These spatial problems are solved by finite elements. The proposed algorithm is useful for spectral analysis of the response of concrete structures exposed to random environmental humidity or temperature, and tremendously reduces the computation time when high frequencies are present in the spectral density of environment.
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References
1.
ASCE Structural Division Task Committee on Finite Element Analysis of Reinforced Concrete (chaired by A. Nilson), “Finite Element Analysis of Reinforced Concrete (State‐of‐the‐Art Report),” ASCE, New York, N.Y., 1982, Chpt. 6, pp. 309–400.
2.
Bažant, Z. P., “Numerical Analysis of Long‐Time Deformations of a Thick‐Walled Concrete Cylinder,” Report No. 69‐12, Structure and Materials Research, Civil Engineering Department, University of California, Berkeley, Calif., Aug., 1969.
3.
Bažant, Z. P., “Numerically Stable Algorithm With Increasing Time Steps for Integral‐Type Aging Creep,” 1st International Conference on Structural Mechanics in React. Tech., Berlin, Vol. 4, Paper H2/3, Sept., 1971.
4.
Bažant, Z. P., “Theory of Creep and Shrinkage in Concrete Structures: A Précis of Recent Developments,” Mechanics Today, Vol. 2, 1–93, Pergamon Press, New York, N.Y., 1975.
5.
Bažant, Z. P., “Mathematical Models for Creep and Shrinkage of Concrete,” Chpt. 7, Creep and Shrinkage in Concrete Structures, Z. P. Bažant and F. H. Wittmann, eds., John Wiley, London, 1982.
6.
Bažant, Z. P., “Response of Aging Linear Systems to Random Input,” Concrete and Geomaterials Report No. 82‐12/665r, Northwestern University, Evanston, Ill., Dec., 1982.
7.
Bažant, Z. P., “Probabilistic Problems in Prediction of Creep and Shrinkage Effects in Structures,” Proc. 4th Int. Conf. on Appl. of Statistics and Probability in Soil and Structural Engineering, G. Augusti, ed., Florence, Italy, June, 1983, pp. 325–356.
8.
Bažant, Z. P., and Asghari, A., “Computation of Age‐Dependent Relaxation Spectra,” Cement and Concrete Research, Vol. 4, 1974, pp. 567–579.
9.
Bažant, Z. P., and Wang, T. S., “Spectral Analysis of Random Shrinkage Stresses in Concrete Structures,” Journal of Engineering Mechanics, ASCE, Vol. 110, No. 2, Feb., 1984, pp. 173–186.
10.
Bažant, Z. P., and Wang, T. S., “Spectral Finite Element Analysis of Random Shrinkage in Concrete Structures,” Journal of Structural Engineering, ASCE, to be published.
11.
Bažant, Z. P., and Wu, S. T., “Rate‐Type Creep Law of Aging Concrete Based on Maxwell Chain,” Materials and Structures, Vol. 7, No. 37, Paris, France, 1974, pp. 45–60.
12.
Cox, H. J., and Armington, J. H., The Weather and Climate of Chicago, The University of Chicago Press, Chicago, Ill., 1914.
13.
Crandall, S. H., Random Vibration in Mechanical Systems, Academic Press, New York, N.Y., 1963.
14.
Davenport, W. B., Probability and Random Processes, McGraw‐Hill, New York, N.Y., 1970.
15.
Fuller, W., An Introduction to Probability Theory with Applications, 2nd ed., Vol. 2, Chapt. 19, John Wiley & Sons, New York, N.Y., 1971.
16.
Neville, A. M., Properties of Concrete, John Wiley, New York, N.Y., 1963.
17.
Neville, A. M., and Dilger, W., Creep of Concrete: Plain, Reinforced Prestressed, North Holland Publ. Co., Amsterdam, 1970.
18.
Newland, D. E., An Introduction to Random Vibration and Spectral Analysis, McGraw Hill, New York, N.Y., 1975.
19.
Papoulis, A., Probability, Random Variables and Stochastic Processes, McGraw‐Hill, New York, N.Y., 1965.
20.
Taylor, R. L., Pister, K. S., and Goudreau, G. L., “Thermo‐mechanical Analysis of Viscoelastic Solids,” International Journal for Numerical Method in Engineering, Vol. 2, 1970, pp. 45–60.
21.
Tsubaki, T., and Bažant, Z. P., “Random Shrinkage Stresses in Aging Viscoelastic Vessel,” Journal of the Engineering Mechanics Division, ASCE, Vol. 108, No. EM3, June, 1982, pp. 527–545.
22.
U.S. Environmental Data Service, “Weather Atlas of the United States,” Gale Research Co., Detroit, Mich., 1975.
23.
Zienkiewicz, O. C., The Finite Element Method, 3rd ed., McGraw‐Hill, New York, N.Y., 1977.
24.
Zienkiewicz, O. C., Watson, M., and King, I. P., “A Numerical Method of Viscoelastic Stress Analysis,” Intern. J. Mech. Sciences, Vol. 10, 1968, pp. 807–827.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 110 • Issue 6 • June 1984
Pages: 972 - 984
Copyright
Copyright © 1984 ASCE.
History
Published online: Jun 1, 1984
Published in print: Jun 1984
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