Handling of Constraints in Finite-Element Response Sensitivity Analysis
Publication: Journal of Engineering Mechanics
Volume 135, Issue 12
Abstract
In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers gratefully acknowledge the support of this research by (1) the National Science Foundation under Grant No. NSFCMS-0010112; (2) the Pacific Earthquake Engineering Research (PEER) Center through the Earthquake Engineering Research Centers Program of the National Science Foundation under Award No. NSFEEC-9701568; and (3) the Louisiana Board of Regents through the Pilot Funding for New Research (Pfund) Program of the National Science Foundation Experimental Program to Stimulate Competitive Research (EPSCoR) under Award No. UNSPECIFIEDNSF(2008)-PFUND-86. The writers wish to thank Dr. Frank McKenna for his invaluable help in implementing the response sensitivity algorithms for handling multi-point constraints in OpenSees. Any opinions, findings, conclusions or recommendations expressed in this publication are those of the writers and do not necessarily reflect the views of the sponsors.
References
Advanced Technology Council (ATC-55). (2005). Evaluation and improvement of inelastic analysis procedure, Advanced Technology Council, Redwood City, Calif.
Barbato, M. (2007). “Finite element response sensitivity, probabilistic response and reliability analyses of structural systems with applications to earthquake engineering.” Ph.D. dissertation, Dept. of Structural Engineering, Univ., of California at San Diego, La Jolla, Calif.
Barbato M., and Conte J. P. (2005). “Finite element response sensitivity analysis: a comparison between force-based and displacement-based frame element models.” Comput. Methods Appl. Mech. Eng., 194(12–16), 1479–1512.
Barbato, M., and Conte, J. P. (2006). “Finite element structural response sensitivity and reliability analyses using smooth versus non-smooth material constitutive models.” Int. J. of Reliability and Safety, 1(1–2), 3–39.
Barbato, M., Zona, A., and Conte, J. P. (2007). “Finite element response sensitivity analysis using three-field mixed formulation: general theory and application to frame structures.” Int. J. Numer. Methods Eng., 69(1), 114–161.
Chopra, A. K. (2001). Dynamics of structures: Theory and applications to earthquake engineering, 2nd Ed., Prentice-Hall, Upper Saddle River, N.J.
Conte, J. P. (2001). “Finite element response sensitivity analysis in earthquake engineering.” Earthquake engineering frontiers in the new millennium, Spencer & Hu, Swets & Zeitlinger, Lisse, The Netherlands, 395–401.
Conte, J. P., Barbato, M., and Spacone, E. (2004). “Finite element response sensitivity analysis using force-based frame models.” Int. J. Numer. Methods Eng., 59(13), 1781–1820.
Conte, J. P., Vijalapura, P. K., and Meghella, M. (2003). “Consistent finite element response sensitivity analysis.” J. Eng. Mech., 129(12), 1380–1393.
Cook, R. D., Malkus, D. S., Plesha, M. E., and Witt, R. J. (2002). Concepts and applications of finite element analysis, 4th Ed., Wiley, New York.
Ditlevsen, O., and Madsen, H. O. (1996). Structural reliability methods, Wiley, New York.
Felippa, C. A. (2001). “Introduction to finite element method.” Ebook, ⟨http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/Home.html⟩ (May 10, 2009).
Franchin, P. (2004). “Reliability of uncertain inelastic structures under earthquake excitation.” J. Eng. Mech., 130(2), 180–191.
Gu, Q. (2008). “Finite element response sensitivity and reliability analysis of soil-foundation-structure-interaction systems.” Ph.D. dissertation, Dept. of Structural Engineering, Univ. of California at San Diego, La Jolla, Calif.
Gu, Q., Conte, J. P., Elgamal, A., and Yang, Z., (2009). “Finite element response sensitivity analysis of multi-yield-surface plasticity model by direct differentiation method.” Comp. Meth. Appl. Mech. Eng. 198(30–32), 2272–2285.
Haukaas, T., and Der Kiureghian, A. (2005). “Parameter sensitivity and importance measures in nonlinear finite element reliability analysis.” J. Eng. Mech., 131(10), 1013–1026.
Haukaas, T., and Der Kiureghian, A. (2007). “Methods and object-oriented software for FE reliability and sensitivity analysis with application to a bridge structure.” J. Comput. Civ. Eng., 21(3), 151–163.
Haukaas, T., and Scott, M. H. (2006). “Shape sensitivities in the reliability analysis of nonlinear frame structures.” Comput. Struc., 84(15–16), 964–977.
Kleiber, M., Antunez, H., Hien, T. D., and Kowalczyk, P. (1997). Parameter sensitivity in nonlinear mechanics: Theory and finite element computations, Wiley, New York.
Mazzoni, S., McKenna, F., and Fenves, G. L. (2005). “OpenSees Command Language Manual.” Pacific Earthquake Engineering Center, University of California, Berkeley, ⟨http://opensees.berkeley.edu/⟩ (May 10, 2009).
Prevost, J. H. (1977). “Mathematical modelling of monotonic and cyclic undrained clay behaviour.” Int. J. Numer. Analyt. Meth. Geomech., 1(2), 195–216.
Scott, B. D., Park, P., and Priestley, M. J. N. (1982). “Stress-strain behavior of concrete confined by overlapping hoops at low and high-strain rates.” J. Am. Concr. Inst., 79(1), 13–27.
Scott, M. H., and Filippou, F. C. (2007). “Response gradients for nonlinear beam-column elements under large displacements.” J. Struct. Eng., 133(2), 155–165.
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.
Scott, M. H., and Haukaas, T. (2008). “Software framework for parameter updating and finite element response sensitivity analysis.” J. Comput. Civ. Eng., 22(5), 281–291.
Zhang, Y., and Der Kiureghian, A. (1993). “Dynamic response sensitivity of inelastic structures.” Comput. Methods Appl. Mech. Eng., 108, 23–36.
Zona, A., Barbato, M., and Conte, J. P. (2004). “Finite element response sensitivity analysis of steel-concrete composite structures.” Rep. No. SSRP-04/02, Dept. of Structural Engineering, Univ. of California, San Diego, Calif.
Zona, A., Barbato, M., and Conte, J. P. (2005). “Finite element response sensitivity analysis of steel-concrete composite beams with deformable shear connection.” J. Eng. Mech., 131(11), 1126–1139.
Zona, A., Barbato, M., and Conte, J. P. (2006). “Finite element response sensitivity analysis of continuous steel-concrete composite girders.” Steel Compos. Struct., 6(3), 183–202.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 12 • December 2009
Pages: 1427 - 1438
Copyright
© 2009 ASCE.
History
Received: Sep 3, 2008
Accepted: Apr 21, 2009
Published online: Apr 24, 2009
Published in print: Dec 2009
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.