Plastic Collapse Modes of Truss Structures under Complex Loading Cycles
Publication: Journal of Engineering Mechanics
Volume 150, Issue 7
Abstract
The kinematic plastic limit, unified shakedown criteria, and reduced kinematic formulation have been utilized to study the plastic collapse modes of truss structures subjected to complex loading cycles. The development from a series of local alternating plastic failures toward the global instantaneous or incremental collapse of the structures with increasing load ranges has been identified. The finite element method and optimization techniques are implemented to effectively solve the resulting mathematical programming problems, with illustrative examples and explanations.
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Data Availability Statement
All data that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 107.02-2021.1.
References
Ampatzis, A., V. Psomiadis, and E. Efthymiou. 2017. “Plastic collapse of hardening spatial aluminium frames: A novel shakedown-based approach.” Eng. Struct. 151 (Nov): 724–744. https://doi.org/10.1016/j.engstruct.2017.08.027.
Bisbos, C., A. Makrodimopoulos, and P. M. Pardalos. 2005. “Second-order cone programming approaches to static shakedown analysis in steel plasticity.” Optim. Methods Software 20 (1): 25–52. https://doi.org/10.1080/1055678042000216003.
Bree, J. 1989. “Plastic deformation of a closed tube due to interaction of pressure stresses and cyclic thermal stresses.” Int. J. Mech. Sci. 31 (11–12): 865–892. https://doi.org/10.1016/0020-7403(89)90030-1.
Ceradini, G. 1980. “Dynamic shakedown in elastic-plastic bodies.” J. Eng. Mech. Div. 106 (3): 481–499. https://doi.org/10.1061/JMCEA3.0002600.
Garcea, G., G. Armentano, S. Petrolo, and R. Casciaro. 2005. “Finite element shakedown analysis of two-dimensional structures.” Int. J. Numer. Methods Eng. 63 (8): 1174–1202. https://doi.org/10.1002/nme.1316.
Gokhfeld, D. 1966. “Some problems of shakedown of plates and shells.” In Vol. 284 of Proc., 6th Soviet Conf. Plates Shells, 284–291. Nauka, Moscow: Baku. Izd.
Gokhfeld, D. A., and O. Charniavsky. 1980. Vol. 4 of Limit analysis of structures at thermal cycling. New York: Springer.
Haghpanah, B., J. Papadopoulos, and A. Vaziri. 2014. “Plastic collapse of lattice structures under a general stress state.” Mech. Mater. 68 (Jan): 267–274. https://doi.org/10.1016/j.mechmat.2013.09.003.
Khoi, V. D., A.-M. Yan, and N.-D. Hung. 2004. “A dual form for discretized kinematic formulation in shakedown analysis.” Int. J. Solids Struct. 41 (1): 267–277. https://doi.org/10.1016/j.ijsolstr.2003.08.013.
Koenig, J. A. 1987. Shakedown of elastic-plastic structures. Amsterdam, Netherlands: Elsevier.
Koiter, W. T. 1960. “General theorems for elastic plastic solids.” In Progress of solid mechanics, 167–221. Amsterdam, Netherlands: North-Holland.
Le, V. C., M. Gilbert, and H. Askes. 2009. “Limit analysis of plates using the EFG method and second-order cone programming.” Int. J. Numer. Methods Eng. 78 (13): 1532–1552. https://doi.org/10.1002/nme.2535.
Le, V. C., H. P. Nguyen, H. Askes, and D. C. Pham. 2017. “A computational homogenization approach for limit analysis of heterogeneous materials.” Int. J. Numer. Methods Eng. 112 (10): 1381–1401. https://doi.org/10.1002/nme.5561.
Le, V. C., T. D. Tran, and D. C. Pham. 2016. “Rotating plasticity and nonshakedown collapse modes for elastic–plastic bodies under cyclic loads.” Int. J. Mech. Sci. 111–112 (Jun): 55–64. https://doi.org/10.1016/j.ijmecsci.2016.04.001.
Leu, S.-Y., and J.-S. Li. 2015. “Shakedown analysis of truss structures with nonlinear kinematic hardening.” Int. J. Mech. Sci. 103 (Nov): 172–180. https://doi.org/10.1016/j.ijmecsci.2015.09.003.
Peng, H., Y. Liu, and H. Chen. 2019. “A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures.” Comput. Mech. 63 (1): 1–22. https://doi.org/10.1007/s00466-018-1581-x.
Pham, D. C. 1997. “Shakedown analysis for trusses and frames.” J. Appl. Mech. Trans. ASME 64 (2): 415–419. https://doi.org/10.1115/1.2787324.
Pham, D. C. 2000. “From local failure toward global collapse of elastic–plastic structures in fluctuating fields.” Int. J. Mech. Sci. 42 (4): 819–829. https://doi.org/10.1016/S0020-7403(98)00137-4.
Pham, D. C. 2007. “Shakedown theory for elastic plastic kinematic hardening bodies.” Int. J. Plast. 23 (7): 1240–1259. https://doi.org/10.1016/j.ijplas.2006.11.003.
Pham, D. C. 2008. “On shakedown theory for elastic–plastic materials and extensions.” J. Mech. Phys. Solids 56 (5): 1905–1915. https://doi.org/10.1016/j.jmps.2007.11.005.
Pham, D. C. 2017. “Consistent limited kinematic hardening plasticity theory and path-independent shakedown theorems.” Int. J. Mech. Sci. 130 (Sep): 11–18. https://doi.org/10.1016/j.ijmecsci.2017.06.005.
Pham, D. C., C. V. Le, and T. D. Tran. 2020. “Shakedown and plastic collapse in plane stress problems.” In Encyclopedia of continuum mechanics, 2231–2240. Berlin: Springer.
Pham, D. C., and H. Stumpf. 1994. “Kinematical approach to the shakedown analysis of some structures.” Q. Appl. Math. 52 (4): 707–719. https://doi.org/10.1090/qam/1306045.
Simon, J.-W. 2013. “Direct evaluation of the limit states of engineering structures exhibiting limited, nonlinear kinematical hardening.” Int. J. Plast. 42 (Mar): 141–167. https://doi.org/10.1016/j.ijplas.2012.10.008.
Simon, J.-W. 2015. “Limit states of structures in n-dimensional loading spaces with limited kinematical hardening.” Comput. Struct. 147 (Jan): 4–13. https://doi.org/10.1016/j.compstruc.2014.09.019.
Simon, J.-W., and D. Weichert. 2012. “Shakedown analysis with multidimensional loading spaces.” Comput. Mech. 49 (4): 477–485. https://doi.org/10.1007/s00466-011-0656-8.
Spiliopoulos, K., and K. Panagiotou. 2017. “An enhanced numerical procedure for the shakedown analysis in multidimensional loading domains.” Comput. Struct. 193 (Dec): 155–171. https://doi.org/10.1016/j.compstruc.2017.08.008.
Tran, T. D., V. C. Le, D. C. Pham, and H. Nguyen-Xuan. 2014. “Shakedown reduced kinematic formulation, separated collapse modes, and numerical implementation.” Int. J. Solids Struct. 51 (15–16): 2893–2899. https://doi.org/10.1016/j.ijsolstr.2014.04.016.
Tran, T. N., G. Liu, H. Nguyen-Xuan, and T. Nguyen-Thoi. 2010. “An edge-based smoothed finite element method for primal–dual shakedown analysis of structures.” Int. J. Numer. Methods Eng. 82 (7): 917–938. https://doi.org/10.1002/nme.2804.
Weichert, D., and G. Maier. 2002. Vol. 432 of Inelastic behaviour of structures under variable repeated loads: Direct analysis methods. Berlin: Springer. https://doi.org/10.1007/978-3-7091-2558-8.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 7 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 20, 2023
Accepted: Jan 25, 2024
Published online: Apr 16, 2024
Published in print: Jul 1, 2024
Discussion open until: Sep 16, 2024
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