Weighted Integral SFEM Including Higher Order Terms
Publication: Journal of Engineering Mechanics
Volume 126, Issue 8
Abstract
The inclusion of the higher order terms in the Taylor's series expansion of the status variable is presented in the formulation for stochastic analysis with the weighted integral method. Generally, in almost all the numerical formulations, omission of the higher order terms is introduced due partly to the complexities of deriving the appropriate simple equations for stochastic analysis or due to the large amount of additional computation time and memory requirement. In this study, the Lagrangian remainder is included in the expansion of the status variable with respect to the mean value of the random variables, which results in simple and efficient formulas for stochastic analysis in the weighted integral method. In the resulting equation, only the “proportionality coefficients” are introduced; thus, no additional computation time or memory requirement is needed. Various examples are investigated to show the efficiency and appropriateness of the suggested formula. The results obtained by the improved weighted integral method equations proposed in this study are reasonable and are in good agreement with those of the Monte Carlo simulation.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Choi, C. K., and Kim, S. H. (1989). “Coupled use of reduced integration and non-conforming modes in quadratic Mindlin plate element.” Int. J. Numer. Methods in Engrs., 28, 1909–1928.
2.
Choi, C. K., Kim, S. H., Park, Y. M., and Chung, K. Y. (1998). “Two-dimensional nonconforming finite elements: a state-of-the-art.” Struct. Engrg. and Mech., 6(1), 41–61.
3.
Choi, C. K., and Noh, H. C. (1996a). “Stochastic finite element analysis of plate structures by weighted integral method.” Struct. Engrg. and Mech., 4(6), 703–715.
4.
Choi, C. K., and Noh, H. C. (1996b). “Stochastic finite element analysis with direct integration method.” Proc., 4th Int. Conf. on Civ. Engrg., Manila, Philippines, 522–531.
5.
Deodatis, G. (1991). “The weighted integral method. I: Stochastic stiffness matrix.”J. Engrg. Mech., ASCE, 117(8), 1851–1864.
6.
Deodatis, G., and Shinozuka, M. (1989). “Bounds on response variability of stochastic systems.”J. Engrg. Mech., ASCE, 115(11), 2543–2563.
7.
Deodatis, G., and Shinozuka, M. (1991). “The weighted integral method. II: Response variability and reliability.”J. Engrg. Mech., ASCE, 117(8), 1865–1877.
8.
Hildebrand, F. B. (1976). Advanced calculus for applications, Prentice-Hall, Englewood Cliffs, N.J.
9.
Kleiber, M., and Hein, T. D. (1992). The stochastic finite element method, Wiley, Chichester, U.K.
10.
Lawrence, M. A. (1987). “Basis random variables in finite element analysis.” Int. J. Numer. Methods in Engrg., 24, 1849–1863.
11.
Liu, K., Belytschiko, T., and Mani, A. (1986). “Probabilistic finite elements for nonlinear structural dynamics.” Comp. Methods in Applied Mech. and Engrg., 56, 61–81.
12.
Park, Y. M., and Choi, C. K. (1997). “The patch tests and convergence for nonconforming Mindlin plate bending elements.” Struct. Engrg. and Mech., 5(4), 471–490.
13.
To, C. S. W. (1986). “The stochastic central difference method in structural dynamics.” Comp. and Struct., 25(6), 813–818.
14.
Yamazaki, F., and Shinozuka, M. (1990). “Simulation of stochastic fields by statistical preconditioning.”J. Engrg. Mech., ASCE, 116(2), 268–287.
15.
Yamazaki, F., Shinozuka, M., and Dasgupta, G. (1988). “Neumann expansion for stochastic finite-element analysis.”J. Engrg. Mech., ASCE, 114(8), 1335–1354.
16.
Zhu, W. Q., Ren, Y. J., and Wu, W. Q. (1992). “Stochastic FEM based on local averages of random vector fields.”J. Engrg. Mech., ASCE, 118(3), 496–511.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 8 • August 2000
Pages: 859 - 866
History
Received: Mar 25, 1999
Published online: Aug 1, 2000
Published in print: Aug 2000
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.