Nonlinear Finite Element Reliability Analysis of Concrete
Publication: Journal of Engineering Mechanics
Volume 122, Issue 12
Abstract
The nonlinear behavior of concrete is complex and is governed by a variety of parameters. As a result, there exist a number of constitutive models that try to predict concrete behavior beyond the linear elastic limit. A mature concrete model must not only remain operational under proportional and nonproportional loadings, but it should be capable of capturing the response behavior in the prepeak and postpeak regimes. Based on such a model, which resorts to an isotropic-hardening description of the prepeak behavior and to a fracture energy-based isotropic-softening description of the postpeak regime, the present paper develops a finite element reliability formulation of nonlinear stochastic concrete under both proportional and nonproportional loadings. The formulation accounts for randomness in loading and spatial variability of concrete properties. The proposed reliability formulation with focus on the prepeak regime uses analytical expressions to compute response gradients. In this manner, efficiency and accuracy concerns associated with perturbation methods are avoided. A computer code is developed for the application of the proposed method to concrete structures. Numerical results are also presented to demonstrate the capability of the computer code to evaluate the reliability of a nondeterministic concrete panel with respect to excessive plastic deformation under both proportional and nonproportional loadings.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bjerager, P. (1989). “On computation methods for structural reliability analysis.”New directions in structural system reliability, D. M. Frangopol, ed., Univ. of Colorado, Boulder, Colo., 52–67.
2.
Deodatis, G.(1990). “Bounds on response variability of stochastic finite element systems.”J. Engrg. Mech., ASCE, 116(3), 565–585.
3.
Deodatis, G.(1991). “Weighted integral method. I: stochastic stiffness matrix.”J. Engrg. Mech., ASCE, 117(8), 1851–1864.
4.
Deodatis, G., and Shinozuka, M.(1989). “Bounds on response variability of stochastic systems.”J. Engrg. Mech., ASCE, 115(11), 2543–2563.
5.
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., 40–52.
6.
Der Kiureghian, A., and Ke, B-J.(1988). “The stochastic finite element method in structural reliability.”Prob. Engrg. Mech., 3(2), 83–91.
7.
Der Kiureghian, A., Li, C-C., and Zhang, Y.(1992). “Recent developments in stochastic finite elements.”Lecture notes in engineering, R. Rackwitz and P. Thoft-Christensen, eds., Springer-Verlag New York, Inc., N.Y., 76, 19–38.
8.
Etse, G., and Willam, K.(1994). “A fracture energy-based constitutive theory for inelastic behavior of plain concrete.”J. Engrg. Mech., ASCE, 120(9), 1983–2011.
9.
Ghanem, R. G., and Spanos, P. D. (1991). Stochastic finite elements: a spectral approach. Springer-Verlag New York, Inc., N.Y.
10.
Lee, Y-H. (1994). “Stochastic finite element analysis of structural plain concrete,” PhD thesis, Dept. of Civ. Engrg., Univ. of Colorado, Boulder, Colo.
11.
Lee, Y.-H., Frangopol, D. M., and Willam, K.(1994). “Probabilistic failure predictions of plain concrete structures on the basis of the extended Leon model.”Proc., 6th Int. Conf. Struct. Safety and Reliability, ICOSSAR 93, G. I. Schuëller, M. Shinozuka, and J. T. P. Yao, eds., A. A. Balkema, Rotterdam, The Netherlands, 1, 391–394.
12.
Lee, Y-H., Frangopol, D. M., and Willam, K. (1995). “Nonlinear finite element reliability analysis of plain concrete under plane stress.”Computational stochastic mechanics, P. D. Spanos, ed., A. A. Balkema, Rotterdam, The Netherlands, 443–450.
13.
Lee, Y-H., Hendawi, S., and Frangopol, D. M. (1993). “RELTRAN: a structural reliability analysis program: version 2.0.”Rep. No. CU/SR-93/6, Struct. Engrg. and Struct. Mech. Res. Ser., Dept. of Civ. Engrg., Univ. of Colorado, Boulder, Colo.
14.
Liu, P-L., and Der Kiureghian, A. (1989). “Finite-element reliability methods for geometrically nonlinear stochastic structures.”Rep. No. UCB/SEMM 89/05, Dept. of Civ. Engrg., Univ. of California, Berkeley, Calif.
15.
Montgomery, K. (1988). “A comparison of concrete constitutive models when applied in finite element analysis,” MS thesis, Dept. of Civ. Engrg., Univ. of Colorado, Boulder, Colo.
16.
Pramono, E., and Willam, K.(1989). “Fracture energy-based plasticity formulation of plain concrete.”J. Engrg. Mech., ASCE, 115(6), 1183–1203.
17.
Teigen, J. G., Frangopol, D. M., Sture, S., and Felippa, C.(1991a). “Probabilistic FEM for nonlinear concrete structures. I: theory.”J. Struct. Engrg., ASCE, 117(9), 2674–2689.
18.
Teigen, J. G., Frangopol, D. M., Sture, S., and Felippa, C.(1991b). “Probabilistic FEM for nonlinear concrete structures. I: applications.”J. Struct. Engrg., ASCE, 117(9), 2690–2707.
19.
Vanmarcke, E. (1983). Random fields: analysis and synthesis. MIT Press, Cambridge, Mass.
20.
Vidal, C. A., and Haber, R. B.(1993). “Design sensitivity analysis for rate-independent elastoplasticity.”Comput. Meth. Appl. Mech. Engrg., 107, 393–431.
21.
Willam, K., and Warnke, P. (1974). “Constitutive model for triaxial behavior of concrete.” Seminar Concrete Struct. Subjected to Triaxial Stresses, ISMES, Bergamo, Italy, IABSE—Rep. No. 19, III, 1–30.
22.
Zhang, Y., and Der Kiureghian, A.(1993). “Dynamic response sensitivity of inelastic structures.”Comput. Meth. Appl. Mech. Engrg., 108, 23–36.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 122 • Issue 12 • December 1996
Pages: 1174 - 1182
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Dec 1, 1996
Published in print: Dec 1996
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.