Response Gradients for Nonlinear Beam-Column Elements under Large Displacements
Publication: Journal of Structural Engineering
Volume 133, Issue 2
Abstract
Accurate and efficient response gradient computations for nonlinear geometry are required in structural reliability, optimization, system identification, and response sensitivity analysis of frame structures that undergo large displacements. In this paper, the exact response gradient of beam-column finite elements under large displacements is derived considering uncertain material and geometric parameters. The element response formulation takes place in a corotational reference frame that displaces and rotates with the element, thus permitting the separation of nonlinear material from nonlinear geometric effects in the computation of the response, as well as of the gradient of the response. Relative to the corotational reference frame, small deformation theory suffices for all structural engineering applications. Thus, the proposed response gradient computations are applicable to most beam-column element formulations available in the literature, including force-based and mixed formulations.
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References
Abramowitz, M., and Stegun, C. A., eds. (1972). Handbook of mathematical functions with formulas, graphs, and mathematical tables, 9th Ed., Dover, New York.
Alemdar, B. N., and White, D. W. (2005). “Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis.” J. Struct. Eng., 131(12), 1811–1819.
Cichon, C. (1984). “Large displacement, in-plane analysis of elastic-plastic frames.” Comput. Struct., 19, 737–745.
Conte, J. P., Vijalapura, P. K., and Meghella, M. (1999). “Consistent finite element sensitivities in seismic reliability analysis.” Proc., 13th ASCE Engineering Mechanics Division Conf., Baltimore.
Crisfield, M. A. (1991). Non-linear finite element analysis of solids and structures, Vol. 1, Wiley, New York.
Demmel, J. W. (1997). Applied numerical linear algebra, SIAM, Philadelphia.
De Souza, R. M. (2000). “Force-based finite element for large displacement inelastic analysis of frames.” Ph.D. thesis, Univ. of California, Berkeley, Calif.
Filippou, F. C., and Fenves, G. L. (2004). “Methods of analysis for earthquake-resistant structures.” Earthquake engineering: From engineering seismology to performance-based engineering, Y. Bozorgnia and V. V. Bertero, eds., CRC, Boca Raton, Fla., Chap. 6.
Franchin, P. (2004). “Reliability of uncertain inelastic structures under earthquake excitation.” J. Eng. Mech., 130(2), 180–191.
Golub, G. H., and Van Loan, C. F. (1996). Matrix computations, 3rd. Ed., Johns Hopkins University Press, Baltimore.
Kleiber, M., Antunez, H., Hien, T. D., and Kowalczyk, P. (1997). Parameter sensitivity in nonlinear mechanics, Wiley, New York.
Liu, P. L., and Der Kiureghian, A. (1991). “Optimization algorithms for structural reliability.” Struct. Safety, 9(3), 161–177.
McKenna, F., Fenves, G. L., and Scott, M. H. (2000). “Open system for earthquake engineering simulation.” ⟨http://opensees.berkeley.edu⟩.
Neuenhofer, A., and Filippou, F. C. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 123(7), 958–966.
Park, M. S., and Lee, B. C. (1996). “Geometrically non-linear and elastoplastic three-dimensional shear flexible beam element of Von-Mises-type hardening material.” Int. J. Numer. Methods Eng., 39, 383–408.
Scott, M. H., and Fenves, G. L. (2006). “Plastic hinge integration methods for force-based beam-column elements.” J. Struct. Eng., 132(2), 244–252.
Scott, M. H., Franchin, P., Fenves, G. L., and Filippou, F. C. (2004). “Response sensitivity for nonlinear beam column elements.” J. Struct. Eng., 130(9), 1281–1288.
Spacone, E., Ciampi, V., and Filippou, F. C. (1996). “Mixed formulation of nonlinear beam finite element.” Comput. Struct., 58(1), 71–83.
Stoer, J., and Bulirsch, R. (1993). Introduction to numerical analysis, 2nd Ed., Springer, New York.
Zhang, Y., and Der Kiureghian, A. (1993). “Dynamic response sensitivity of inelastic structures.” Comput. Methods Appl. Mech. Eng., 108, 23–36.
Zienkiewicz, O. C., and Taylor, R. L. (2000). The finite element method: Volume 1, the basis, 5th Ed., Butterworth-Heinman, Stoneham, Mass.
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© 2007 ASCE.
History
Received: May 18, 2005
Accepted: Nov 28, 2005
Published online: Feb 1, 2007
Published in print: Feb 2007
Notes
Note. Associate Editor: Keith D. Hjelmstad
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