Explicit Fiber Beam-Column Elements for Impact Analysis of Structures
Publication: Journal of Structural Engineering
Volume 144, Issue 7
Abstract
The solution of impact problems requires advanced computational techniques to overcome the difficulties associated with large short-duration loads. Such cases typically use the explicit time integration method because it provides a stable solution for problems such as the analysis of structures subjected to shock and impact loads. However, most explicit-based finite elements were developed for continuum models such as membrane and solid elements, which renders the problem computationally expensive. On the other hand, the development of fiber-based beam finite elements allows for the simulation of the global structural behavior with very few degrees of freedom, while accounting for the detailed material nonlinearity along the element length. However, explicit-based fiber beam elements have not been properly formulated, in particular for the case of the emerging force-based beam element. This paper develops two fiber plane beam elements that consider an explicit time integration scheme for the solution of the dynamic equation of motion. The first element uses a displacement-based formulation, whereas the second element uses a force-based formulation. For the latter case, a new algorithm that eliminates the need for iterations at the element level is proposed. The developed elements require the use of a lumped mass matrix and a small time increment to ensure numerical stability. No iterations or convergence checks are required, which renders the problem numerically efficient. The developed explicit fiber beam-column models, particularly the force-based element, represent a simple yet powerful tool for simulating the nonlinear complex effect of impact loads on structures accurately while using very few finite elements. The traditional implicit method of analysis typically fails to provide numerically stable behavior for such short-duration problems. Two correlation studies are presented to highlight the efficiency of the developed elements in modeling impact problems in which the material models consider the strain rate effect. These examples confirm the accuracy and efficiency of the presented elements.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alemdar, B., and D. White. 2005. “Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis.” J. Struct. Eng. 131 (12): 1811–1819.
Ammann, W., M. Muehlematter, and H. Bachmann. 1982. “Stress-strain behaviour of non-prestressed and prestressed reinforcing steel at high strain rates.” In Proc., RILEM-CEB-IABSE-IASS, Concrete Structures under Impact and Impulsive Loading, 656. Berlin: BAM.
Bathe, K., and A. Cimento. 1980. “Some practical procedures for the solution of nonlinear finite element equations.” Comput. Methods Appl. Mech. Eng. 22 (1): 59–85.
Chang, S. 2009. “An explicit method with improved stability property.” Int. J. Numer. Methods Eng. 77 (8): 1100–1120.
Chen, L., Y. Xiao, and S. El-Tawil. 2016. “Impact tests of model RC columns by an equivalent truck frame.” J. Struct. Eng. 142 (5): 04016002.
Felippa, C. 2013. “Matrix finite element methods in dynamics (course in preparation).” Accessed December 6, 2016. https://www.colorado.edu/engineering/CAS/courses.d/MFEMD.d/.
Filippou, F. C., E. P. Popov, and V. V. Bertero. 1983. Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. Berkeley, CA: Univ. of California.
Fujikake, K., B. Li, and S. Soeun. 2009. “Impact response of reinforced concrete beam and its analytical evaluation.” J. Struct. Eng. 135 (8): 938–950.
Fulei, W., and L. Yungui. 2011. “A nonlinear dynamic beam element with explicit algorithms.” Commun. Comput. Inf. Sci. 163: 311–318.
Gu, L., and S. Wu. 2013. Introduction to the explicit finite element method for nonlinear transient dynamics, 5. Hoboken, NJ: Wiley.
Hong, S. G., S. J. Lee, and M. J. Lee. 2014. “Steel plate concrete walls for containment structures in Korea: In-plane shear behavior.” Infrastruct. Syst. Nucl. Energy 105: 237–257.
Hrynyk, T., and F. Vecchio. 2014. “Behavior of steel fiber-reinforced concrete slabs under impact load.” ACI Struct. J. 111 (5): 1213–1223.
Huang, C., and T. Wu. 2009. “A study on dynamic impact of vertical concrete cask tip-over using explicit finite element analysis procedures.” Ann. Nucl. Energy 36 (2): 213–221.
Kent, D. C., and R. Park. 1971. “Flexural members with confined concrete.” J. Struct. Eng. 97 (7): 1969–1990.
Kujawski, J. 1988. “Stable semi-explicit algorithms for non-linear dynamic problems.” Earthquake Eng. Struct. Dyn. 16 (6): 855–865.
Limberger, E., K. Brandes, and J. Herter. 1982. “Influence of mechanical properties of reinforcing steel on the ductility of reinforced concrete beams with respect to high strain rates.” In Concrete structures under impact and impulsive loading, edited by G. Plauk, 656. Berlin: BAM.
Lok, T., and P. Zhao. 2004. “Impact response of steel fiber-reinforced concrete using a split Hopkinson pressure bar.” J. Mater. Civ. Eng. 16 (1): 54–59.
Malvar, L. 1998. “Review of static and dynamic properties of steel reinforcing bars.” ACI Mater. J. 95 (5): 609–616.
Menegotto, M., and P. E. Pinto. 1973. “Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and nonelastic behavior of elements under combined normal force and bending.” In IABSE Symp. on Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads. Zurich, Switzerland: International Association for Bridge and Structural Engineering.
Miranda, I., R. Ferencz, and T. Hughes. 1989. “An improved implicit-explicit time integration method for structural dynamics.” Earthquake Eng. Struct. Dyn. 18 (5): 643–653.
Mullapudi, T., and A. Ayoub. 2010. “Modeling of the seismic behavior of shear-critical reinforced concrete columns.” Eng. Struct. 32 (11): 3601–3615.
Neuenhofer, A., and F. Filippou. 1997. “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng. 123 (7): 958–966.
Pezeshk, S., and C. Camp. 1995. “An explicit time integration technique for dynamic analyses.” Int. J. Numer. Methods Eng. 38 (13): 2265–2281.
Ross, C. A., P. Y. Thompson, and J. W. Tedesco. 1989. “Split-Hopkinson pressure-bar tests on concrete and mortar in tension and compression.” ACI Mater. J. 86 (5): 475–481.
Saatci, S., and F. Vecchio. 2009. “Effects of shear mechanisms on impact behavior of reinforced concrete beams.” ACI Struct. J. 106 (1): 78–86.
Scott, B. D., R. Park, and M. J. N. Priestley. 1982. “Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates.” ACI J. 79 (1): 13–27.
Spacone, E., F. Filippou, and F. Taucer. 1996. “Fibre beam-column model for non-linear analysis of R/C frames. Part I: Formulation.” Earthquake Eng. Struct. Dyn. 25 (7): 711–725.
Sun, J., K. Lee, and H. Lee. 2000. “Comparison of implicit and explicit finite element methods for dynamic problems.” J. Mater. Process. Technol. 105 (1–2): 110–118.
Taylor, R. 2014. FEAP: Finite element analysis program. Berkeley, CA: Univ. of California.
Tenek, L. 2015. “A beam finite element based on the explicit finite element method.” Int. Rev. Civ. Eng. 6 (5): 124.
Yang, D., D. Jung, I. Song, D. Yoo, and J. Lee. 1995. “Comparative investigation into implicit, explicit, and iterative implicit/explicit schemes for the simulation of sheet-metal forming processes.” J. Mater. Process. Technol. 50 (1–4): 39–53.
Yoshida, Y., N. Masuda, T. Morimoto, and N. Hirosawa. 1980. “An incremental formulation for computer analysis of space framed structures.” [In Japanese.] J. Struct. Mech. Earthquake Eng. 300 (Aug): 21–32.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Jan 24, 2017
Accepted: Dec 13, 2017
Published online: Apr 19, 2018
Published in print: Jul 1, 2018
Discussion open until: Sep 19, 2018
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.