Structural Response Variability III
Publication: Journal of Engineering Mechanics
Volume 115, Issue 8
Abstract
The response variability of statically indeterminate linear structures due to spatial variation of material or geometry properties, or both, is investigated. Utilizing a Green's function formulation or the more general flexibility method, the mean square response of statically indeterminate beams and frames (multistory/multibay) is determined without recourse to a finite element analysis. The response variability is expressed in terms of random variables even though the material or the geometric property, or both, (in this case the fiexibility) are considered to constitute stochastic fields. This makes it easier to estimate not only the response statistics but also the limit state probability, if the limit state conditions are given. The response variability can be estimated by various methods, including the first‐order second moment method and Monte Carlo simulation techniques. Finally, the safety index for the beam midspan deflection and end moment are evaluated using standard methods.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bucher, C. G., and Shimozuka, M. (1986). “Structural Response Variability II,” J. Engrg. Mech., ASCE, Vol. 114, No. 12, pp. 2035–2054.
2.
Der Kiureghian, A. (1985). “Finite element methods in structural safety studies.” Structural safety studies, J. T.‐P. Yao et al., eds., ASCE, New York, N.Y.
3.
Handa, K., and Anderson, K. (1981). “Applications of finite element methods in the statistical analysis of structures.” Proc. of the 3rd ICOSSAR, Trondheim, Norway.
4.
Hisada, T., and Nakagiri, S. (1980). “A note on stochastic finite element method (part 2)—variation of stress and strain caused by fluctuations of material properties and geometrical boundary conditions.” J. Inst. Ind. Sci., Univ. of Tokyo, Tokyo, Japan, 32(5).
5.
Lawrence, M., Liu, W. K., and Belytschko, T. (1986). “Stochastic finite element analysis for linear and nonlinear structural response.” Abstracts, Structures Congress '86, New Orleans, La., 337.
6.
Liu, W. K., Belytschko, T., and Mani, A. (1985). “A computational method for the determination of the probabilistic distribution of the dynamic response of structures.” Proc. of the 1985 Pressure Vessels and Piping Conference, New Orleans, La., 243–248.
7.
Rackwitz, R., and Fiessler, B. (1977). “An algorithm for the calculation of structural reliability under combined loading.” Heft 17, Technische Universitat Munchen, Munich, W. Germany.
8.
Shinozuka, M. (1972a). “Monte Carlo solution of structural dynamics.” Int. J. Comput. Struct., 2, 855–874.
9.
Shinozuka, M. (1972b). “Probabilistic modeling of concrete structures.” J. Engrg. Mech. Div., ASCE, 98(6), 1433–1451.
10.
Shinozuka, M. (1974). “Digital simulation of random processes in engineering mechanics with the aid of FFT technique.” Stochastic probletns in mechanics, S. T. Ariaratnam and H. H. E. Leipholz, eds., Univ. of Waterloo, Waterloo, Ont., Canada, 277–286.
11.
Shinozuka, M. (1983). “Basic analysis of structural safety.” J. Struct. Engrg., ASCE, 109(3).
12.
Shinozuka, M. (1985a). “Stochastic fields and their digital simulation.” Lecture notes for the CISM Course on Stochastic Methods in Structural Mechanics, Udine, Italy; also in Stochastic Mechanics—Vol. I. M. Shinozuka, ed., Columbia University, New York, N.Y., 1987, 1–44.
13.
Shinozuka, M. (1985b). “Response variability due to spatial randomness.” Proc. of the 2nd Int. Workshop on Stochastic Methods in Struct. Mech., SEAG, Pavia, Italy.
14.
Shinozuka, M. (1986). “Structural response variability.” J. Engrg. Mech., ASCE, 113(6), 825–842.
15.
Shinozuka, M., and Dasgupta, G. (1986). “Stochastic finite element methods in dynamics.” Proc. of the 3rd Conference on Dynamic Response of Structures, Los Angeles, Calif., 44–54.
16.
Shinozuka, M., and Jan, C.‐M. (1972). “Digital simulation of random processes and its applications.” J. Sound Vib., 25(1), 111–128.
17.
Shinozuka, M., and Lenoe, E. (1976). “A probabilistic model for spatial distribution of material properties.” J. of Engrg. Fracture Mech., 8, 217–227.
18.
Shinozuka, M., and Wen, Y.‐K. (1972). “Monte Carlo solution of nonlinear vibrations.” AIAA J., 10(1), 37–40.
19.
Vaicaitis, R., Jan, C.‐M., and Shinozuka, M. (1972). “Nonlinear panel response from a turbulent boundary layer.” AIAA J., 10(7), 895–899.
20.
Vaicaitis, R., Shinozuka, M., and Takeno, M. (1975). “Response analysis of tall buildings to wind loadings.” J. Struct. Div., ASCE, 101(3), 585–600.
21.
Vanmarcke, E., and Grigoriu, M. (1983). “Stochastic finite element analysis of simple beams.” J. Engrg. Mech., ASCE, 109(5), 1203–1214.
22.
Vanmarcke, E. (1983). Random fields. MIT Press, Cambridge, Mass.
23.
Yamazaki, F., et al. (1985). “Neumann expansion for stochastic finite element analysis.” J. Engrg. Mech., ASCE, Vol. 114, No. 8, pp. 1335–1354.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Aug 1, 1989
Published in print: Aug 1989
Authors
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.