Response Prediction of Geometrically Nonlinear Structures
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VIEW THE REPLYPublication: Journal of Structural Engineering
Volume 126, Issue 11
Abstract
The response prediction of geometrically nonlinear elastic structures (GNS) is an important area of research in structural engineering and mechanics. Also, in professional practice it has become mandatory to carry out such an evaluation for long-span and slender structures such as suspension bridges. However, this is often a very difficult task, especially when randomness in loads and material properties have to be taken into account. In this study, the responses of GNS are obtained using the total Lagrangian formulation for finite-element discretization. In the presence of uncertainties, the mean and variance of the response of GNS are evaluated by first-order approximation and Monte Carlo simulation. Numerical examples are presented to illustrate the computational process and to study the effects of various parameters such as type of analysis (linear or nonlinear), magnitude of loads and load effects, and type of approximation (first order or simulation) on the main descriptors of the response of GNS. For the cases studied, the results show that first-order approximation and Monte Carlo simulation are in close agreement. This indicates that, at least for the numerical examples presented, first-order approximation can be used in place of Monte Carlo simulation. In this manner, computational time is drastically reduced without a significant loss in accuracy.
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References
1.
Ang, A. H.-S., and Tang, W. H. ( 1975). Probability concepts in engineering planning and design, Vol. 1, Wiley, New York.
2.
Bathe, K.-J. ( 1982). Finite element procedures in engineering analysis, Prentice-Hall, Englewood Cliffs, N.J.
3.
Crisfield, M. A. ( 1991). Non-linear finite element analysis of solid and structures, Wiley, Chichester, U.K.
4.
Der Kiureghian, A., and Ke, J.-B. ( 1988). “The stochastic finite element method in structural reliability.” Probabilistic Engrg. Mech., 3(2), 83–91.
5.
Enright, M. P. ( 1998). “Time-variant reliability of reinforced concrete bridges under environmental attack.” PhD thesis, Dept. of Civ., Envir., and Arch. Engrg., University of Colorado, Boulder, Colo.
6.
Estes, A. C., and Frangopol, D. M. ( 1998). “RELSYS: A computer program for structural system reliability.” Struct. Engrg. and Mech., 6(8), 901–919.
7.
Frangopol, D. M., and Imai, K. ( 2000). “Geometrically nonlinear finite element reliability analysis of structural systems. II: applications.” Comp. and Struct., 77(6), 693–709.
8.
Hisada, T., and Nakagiri, S. ( 1985). “Role of the stochastic finite element method in structural safety and reliability.” Structural safety and reliability, Vol. 1, I. Konishi, A. H.-S. Ang, and M. Shinozuka, eds., IASSAR, Kyoto, Japan, 385–394.
9.
Imai, K. ( 1999). “Reliability analysis of geometrically nonlinear structures with application to suspension bridges.” PhD thesis, Dept. of Civ., Envir., and Arch. Engrg., University of Colorado, Boulder, Colo.
10.
Imai, K., and Frangopol, D. M. ( 1999). “Finite element reliability-based assessment of an existing suspension bridge using geometrically nonlinear analysis.” Case studies in optimal design and maintenance planning of civil infrastructure systems. D. M. Frangopol, ed., ASCE, Reston, Va., 117–135.
11.
Imai, K., and Frangopol, D. M. ( 2000). “Geometrically nonlinear finite element reliability analysis of structural systems. I: theory.” Comp. and Struct., 77(6), 677–691.
12.
Kanchi, M. B. ( 1993). Matrix methods of structural analysis, Wiley Eastern Ltd., New Delhi.
13.
Liu, P.-L., and Der Kiureghian, A. ( 1989). “Finite element reliability methods for geometrically nonlinear structures.” Rep. No. UCB/SEMM-89/05, Struct. Engrg., Mech., and Mat., Dept. of Civ. Engrg., University of California, Berkeley, Calif.
14.
Liu, P.-L., and Der Kiureghian, A. (1991). “Finite element reliability of geometrically nonlinear uncertain structures.”J. Engrg. Mech., ASCE, 117(8), 1806–1825.
15.
Ryu, Y. S., Haririan, M., Wu, C. C., and Arora, J. S. ( 1985). “Structural design sensitivity analysis of nonlinear response.” Comp. and Struct., 21(1/2), 245–255.
16.
Taylor, R. L. ( 1996). FEAP–A finite element analysis program, Version 6.0, Dept. of Civ. Engrg., University of California, Berkeley, Calif.
17.
Wu, C. C., and Arora, J. S. ( 1987). “Design sensitivity analysis and optimization of nonlinear structural response using incremental procedure.” AIAA J., 25(8), 1118–1125.
18.
Zienkiewicz, O. C., and Taylor, R. L. ( 1991). The finite element method, 4th Ed., Vol. 2, McGraw-Hill, Berkshire, U.K.
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Published In
Journal of Structural Engineering
Volume 126 • Issue 11 • November 2000
Pages: 1348 - 1355
History
Received: Mar 1, 1999
Published online: Nov 1, 2000
Published in print: Nov 2000
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