Response Sensitivity of Geometrically Nonlinear Force-Based Frame Elements
Publication: Journal of Structural Engineering
Volume 139, Issue 11
Abstract
To expand the scope of accurate and efficient gradient-based applications in structural engineering, the direct differentiation method (DDM) is applied to compute the response sensitivity of force-based frame finite elements with combined material and geometric nonlinearity where the transverse displacement field is determined by curvature-based displacement interpolation. Sensitivity is developed for element-level parameters including constitutive properties, cross-section dimensions, and integration points and weights, as well as structural-level parameters corresponding to nodal coordinates. The response sensitivity is found to be significantly more complicated than for geometrically linear force-based elements because it requires the derivative of the transverse displacement field under the condition of fixed basic forces. Finite-difference calculations verify the DDM sensitivity equations for material and geometric nonlinear force-based element response while reliability analysis of a gravity-loaded steel frame demonstrates the efficiency of the DDM sensitivity in a gradient-based application.
Get full access to this article
View all available purchase options and get full access to this article.
References
Addessi, D., and Ciampi, V. (2007). “A regularized force-based beam element with a damage-plastic section constitutive law.” Int. J. Numer. Methods Eng., 70(5), 610–629.
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.
Bebamzadeh, A., and Haukaas, T. (2008). “Second-order sensitivities of inelastic finite-element response by direct differentiation.” J. Eng. Mech., 134(10), 867–880.
Buonopane, S. G. (2008). “Strength and reliability of steel frames with random properties.” J. Struct. Eng., 134(2), 337–344.
Calabrese, A., Almeida, J. P., and Pinho, R. (2010). “Numerical issues in distributed inelasticity modeling of RC frame elements for seismic analysis.” J. Earthquake Eng., 14(1), 38–68.
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 Meghalla, M. (2003). “Consistent finite-element response sensitivity analysis.” J. Eng. Mech., 129(12), 1380–1393.
Crisfield, M. A. (1991). Non-linear finite element analysis of solids and structures, Vol. 1, Wiley, West Sussex, U.K.
De Souza, R. M. (2000). “Force-based finite element for large displacement inelastic analsysis of frames.” Ph.D. thesis, Univ. of California at Berkeley, Berkeley, CA.
Ditlevsen, O., and Madsen, O. H. (1996). Structural reliability methods, Wiley, New York.
Filippou, F. C., and Fenves, G. L. (2004). “Methods of analysis for earthquake-resistant structures.” Chapter 6, Earthquake engineering: From engineering seismology to performance-based engineering, Y. Bozorgnia and V. V. Bertero, eds., CRC, Boca Raton, FL.
Golub, G. H., and Van Loan, C. F. (1996). Matrix computations, 3rd Ed., Johns Hopkins University Press, Baltimore.
Gu, Q., Barbato, M., and Conte, J. P. (2009). “Handling of constraints in finite-element response sensitivity analysis.” J. Eng. Mech., 135(12), 1427–1438.
Haukaas, T. (2006). “Efficient computation of response sensitivities for inelastic structures.” J. Struct. Eng., 132(2), 260–266.
Hjelmstad, K. D., and Taciroglu, E. (2005). “Variational basis of nonlinear flexibility methods for structural analysis of frames.” J. Eng. Mech., 131(11), 1157–1169.
Jafari, V., Vahdani, S., and Rahimian, M. (2010). “Derivation of the consistent flexibility matrix for geometrically nonlinear Timoshenko frame finite element.” Finite Elem. Anal. Design, 46(12), 1077–1085.
Jeffers, A. E., and Sotelino, E. D. (2010). “Analysis of structures in fire using a flexibility-based finite element.” 2010 structures congress, ASCE, Reston, VA, 2186–2197.
Maleck, A. E. (2001). “Second-order inelastic and modified elastic analysis and design evaluation of planar steel frames.” Ph.D. thesis, Georgia Institute of Technology, Atlanta.
McKenna, F., Scott, M. H., and Fenves, G. L. (2010). “Nonlinear finite-element analysis software architecture using object composition.” J. Comput. Civ. Eng., 24(1), 95–107.
Neuenhofer, A., and Filippou, F. C. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 123(7), 958–966.
Neuenhofer, A., and Filippou, F. C. (1998). “Geometrically nonlinear flexibility-based frame finite element.” J. Struct. Eng., 124(6), 704–711.
Pajot, J. M., and Maute, K. (2006). “Analytical sensitivity analysis of geometrically nonlinear structures based on the co-rotational finite element method.” Finite Elem. Anal. Design, 42(10), 900–913.
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., and Filippou, F. C. (2007). “Exact response gradients for large displacement nonlinear beam-column elements.” 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.
Spacone, E., Filippou, F. C., and Taucer, F. F. (1996). “Fiber beam-column model for nonlinear analysis of R/C frames: Formulation.” Earthquake Eng. Struct. Dyn., 25(7), 711–725.
Welch, B. B. (2000). Practical programming in Tcl and Tk, Prentice Hall, Upper Saddle River, NJ.
Zhang, Y., and Der Kiureghian, A. (1993). “Dynamic response sensitivity of inelastic structures.” Comput. Methods Appl. Mech. Eng., 108(1–2), 23–36.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 139 • Issue 11 • November 2013
Pages: 1963 - 1972
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Apr 6, 2012
Accepted: Oct 11, 2012
Published online: Oct 13, 2012
Published in print: Nov 1, 2013
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.