Plastic Deformations of Impulsively Loaded, Rigid-Plastic Beams
Publication: Journal of Engineering Mechanics
Volume 126, Issue 2
Abstract
Rigid body dynamics is used to determine the deformation of a fixed-end, rigid-plastic beam subjected to uniformly distributed impulsive loading. The proposed solution methodology allows calculations of deformations at plastic hinges and can be used to establish rigid-plastic fracture criteria for rigid-plastic beams. Unlike previous solutions to this problem, rotary inertia and the shear deformations at the support are considered. The solution for beam deformations is described in three phases: shear, bending, and membrane. Each phase ends when the corresponding component of the strain rate vector vanishes. The initial shear phase is completed when the transverse shear velocity at the support vanishes. The beam then undergoes only rigid body rotation and axial stretching at plastic hinges in the bending phase. The bending phase ends when the angular velocity vanishes. In the membrane phase, the beam acts like a string until the transverse velocity vanishes. It has been found that beams subjected to low impulse velocity attain permanent deformation in the bending phase, while beams subjected to high impulse velocity reach permanent deformation in the membrane phase. The predictions of the beam deflections using the proposed methodology are within 15% of the experimental results.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Jones, N. (1967). “The influence of strain-hardening and strain-rate sensitivity on the permanent deformation of impulsively-loaded rigid-plastic beams.” Int. J. Mech. Sci., 9(12), 777–796.
2.
Jones, N. (1989). Structural impact. Cambridge University Press, Cambridge, U.K.
3.
Jones, N., Griffin, R. N., and Van Duzer, R. E. (1971). “An experimental study into the dynanic plastic behavior of wide beams and rectangular plates.” Int. J. Mech. Sci., 13, 721–735.
4.
Sobotka, Z. (1955). Theorie Plasticite, t. I-II, CSAV, Prague, Czech Republic.
5.
Stronge, W. J., and Yu, T. X. (1993). Dynamic models for structural plasticity. Springer, London.
6.
Symonds, P. S. (1954). “Large plastic deformations of beams under blast type loading.” Proc., 2nd US Nat. Congr. Appl. Mech., ASME, New York, 505–515.
7.
Symonds, P. S. ( 1965). “Viscoplastic behavior in response of structures to dynamic loading,” Behavior of materials under dynamic loading, N. J. Huffington, ed., ASME, New York, 106–124.
8.
Symonds, P. S., and Mentel, T. J. (1958). “Impulsive loading of plastic beams with axial constraint,” J. Mech. Phys. Solids, 6, 186–202.
9.
Vaziri, R., Olson, M. D., and Anderson, D. L. (1987). “Dynamic response of axially constrained plastic beams to blast loads.” Int. J. Solids and Struct., 23(1), 153–174.
10.
Yu, J., and Jones, N. (1991). “Further experimental investigation on the failure of clamped beams under impact loads.” Int. J. Solids and Struct., 27(9), 1113–1137.
Information & Authors
Information
Published In
History
Received: Aug 20, 1998
Published online: Feb 1, 2000
Published in print: Feb 2000
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.