Dynamic Performance of Simply Supported Rigid Plastic Circular Thick Steel Plates Subjected to Localized Blast Loading
Publication: Journal of Engineering Mechanics
Volume 140, Issue 1
Abstract
Close-in explosive charges, such as improvised explosive devices, produce localized blast loadings that can potentially cause damage to property in military and civil structures and/or loss of life. Because the localized short-duration blast pulse affects most severely a small area of a plated structure, the plate’s boundary effects are not as influential as they would be when quasi-static or even a global blast loading is applied, and thus full plate action may not be used. Many common structural forms are composed of individual plated elements, and thus the investigation of localized blast loading effects on plates is an important aspect that leads to understanding the integral behavior. Typically, plates are made of ductile metallic materials, such as steel, which exhibit considerable postyield deformation capacity when subjected to such extreme dynamic loads. An analytical study of the dynamic plastic response of rigid plastic plated structures is the aim of the current study. A circular plate is studied in the present work, and a general form of a localized blast loading function with a spatial variation having a central radial zone with constant pressure and exponentially decaying profile outside the zone is assumed. Assuming that steel exhibits perfectly plastic behavior and considering transverse shear and rotatory inertia effects, using the approach developed previously, results for the permanent transverse displacements and response durations are found in terms of an applied impulsive velocity, which is a function of the applied localized blast load. It is found that the influence of transverse shear is only relevant for small values of , or plate radius-to-thickness ratio, which do not correspond to typical plate geometries found in plated structures subjected to blast loading. Both midpoint and support displacement are only significantly affected by transverse shear effects for . The same argument is extended to inclusion of rotatory inertia. It is also seen that, for close-in blasts, the effects of transverse shear and rotatory inertia are irrelevant, even for small values of .
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work is part of a research project jointly funded by the Defence Science and Technology Laboratory and the Engineering and Physical Sciences Research Council, both in the United Kingdom.
References
Aggarwal, H. R., and Ablow, C. M. (1971). “Plastic bending of an annular plate by uniform impulse.” Int. J. Non-linear Mech., 6(1), 69–80.
ANSYS 12.0 [Computer software]. Canonsburg, PA, ANSYS.
Babaei, H., and Darvizeh, A. (2012). “Analytical study of plastic deformation of clamped circular plates subjected to impulsive loading.” J. Mech. Mater. Struct., 7(4), 309–322.
Balden, V. H., and Nurick, G. N. (2005). “Numerical simulation of the post-failure motion of steel plates subjected to blast loading.” Int. J. Impact Eng., 32(1–4), 14–34.
Batra, R. C., and Dubey, R. N. (1971). “Impulsively loaded circular plates.” Int. J. Solids Struct., 7(8), 965–978.
Bonorchis, D., and Nurick, G. N. (2009). “The influence of boundary conditions on the loading of rectangular plates subjected to localised blast loading: Importance in numerical simulations.” Int. J. Impact Eng., 36(1), 40–52.
Børvik, T., Dey, S., and Clausen, A. H. (2009). “Perforation resistance of five different high-strength steel plates subjected to small-arms projectiles.” Int. J. Impact Eng., 36(7), 948–964.
Chung Kim Yuen, S., et al. (2008). “Deformation of mild steel plates subjected to large-scale explosions.” Int. J. Impact Eng., 35(8), 684–703.
Chung Kim Yuen, S., and Nurick, G. N. (2005). “Experimental and numerical studies on the response of quadrangular stiffened plates. Part I: subjected to uniform blast load.” Int. J. Impact Eng., 31(1), 55–83.
Conroy, M. F. (1969). “Rigid-plastic analysis of a simply supported circular plate due to dynamic circular loading.” J. Franklin Inst., 288(2), 121–135.
Cox, A. D., and Morland, L. W. (1959). “Dynamic plastic deformations of simply-supported square plates.” J. Mech. Phys. Solids, 7(4), 229–241.
Florence, A. L. (1965). “Annular plate under a transverse line impulse.” AIAA J., 3(9), 1726–1732.
Florence, A. L. (1966a). “Circular plate under a uniformly distributed impulse.” Int. J. Solids Struct., 2(1), 37–47.
Florence, A. L. (1966b). “Clamped circular rigid-plastic plates under central blast loading.” Int. J. Solids Struct., 2(2), 319–335.
Florence, A. L. (1977). “Response of circular plates to central pulse loading.” Int. J. Solids Struct., 13(11), 1091–1102.
Gharababaei, H., and Darvizeh, A. (2010). “Experimental and analytical investigation of large deformation of thin circular plates subjected to localised and uniform impulsive loading.” Mech. Based Design Struct. Machines, 38(2), 171–189.
Gharababaei, H., Darvizeh, A., and Darvizeh, M. (2010a). “Analytical and experimental studies for deformation of circular plates subjected to blast loading.” J. Mech. Sci. Technol., 24(9), 1855–1864.
Gharababaei, H., Nariman-zadeh, N., and Darvizeh, A. (2010b). “A simple modelling method for deflection of circular plates under impulsive loading using dimensionless analysis and singular value decomposition.” J. Mech. Mater. Struct., 26, 355–361.
Gupta, N. K., and Nagesh (2007). “Deformation and tearing of circular plates with varying support conditions under uniform impulsive loads.” Int. J. Impact Eng., 34(1), 42–59.
Hooke, R., and Rawlings, B. (1969). “An experimental investigation of the behaviour of clamped, rectangular mild steel plates subjected to uniform transverse pressure.” Proc., Inst. Civ. Eng., 42(1), 75–103.
Hopkins, H. G., and Prager, W. (1953). “The load carrying capacities of circular plates.” J. Mech. Phys. Solids, 2(1), 1–13.
Hopkins, H. G., and Prager, W. (1954). “On the dynamics of plastic circular plates.” Z. Angew. Math. Phys., 5(4), 317–330.
Jacob, N., Chung Kim Yuen, S., Nurick, G. N., Bonorchis, D., Desai, S. A., and Tait, D. (2004). “Scaling aspects of quadrangular plates subjected to localised blast loads - experiments and predictions.” Int. J. Impact Eng., 30(8–9), 1179–1208.
Jacob, N., Nurick, G. N., and Langdon, G. S. (2007). “The effect of stand-off distance on the failure of fully clamped circular mild steel plates subjected to blast loads.” Eng. Struct., 29(10), 2723–2736.
Jones, N. (1968a). “Finite deflections of a simply supported rigid-plastic annular plate loaded dynamically.” Int. J. Solids Struct., 4(6), 593–603.
Jones, N. (1968b). “Impulsive loading of a simply supported circular rigid plastic plate.” J. Appl. Mech., 35(1), 59–65.
Jones, N. (1969). “Combined distributed loads on rigid-plastic circular plates with large deflections.” Int. J. Solids Struct., 5(1), 51–64.
Jones, N. (1971). “A theoretical study of the dynamic plastic behavior of beams and plates with finite-deflections.” Int. J. Solids Struct., 7(8), 1007–1029.
Jones, N. (1989). Structural impact, Cambridge University Press, Cambridge, U.K.
Jones, N., and Gomes de Oliveira, J. (1980). “Dynamic plastic response of circular plates with transverse shear and rotatory inertia.” J. Appl. Mech., 47(1), 27–34.
Jones, N., Griffin, R. N., and Van Duzer, R. E. (1971). “An experimental study into the dynamic plastic behaviour of wide beams and rectangular plates.” Int. J. Mech. Sci., 13(8), 721–735.
Jones, N., Uran, T. O., and Tekin, S. A. (1970). “The dynamic plastic behavior of fully clamped rectangular plates.” Int. J. Solids Struct., 6(12), 1499–1512.
Jones, N., and Wierzbicki, T. (1987). “Dynamic plastic failure of a free-free beam.” Int. J. Impact Eng., 6(3), 225–240.
Karagiozova, D., Langdon, G. S., Nurick, G. N., and Chung Kim Yuen, S. (2010). “Simulation of the response of fibre-metal laminates to localised blast loading.” Int. J. Impact Eng., 37(6), 766–782.
Langdon, G. S., Yuen, S. C. K., and Nurick, G. N. (2005). “Experimental and numerical studies on the response of quadrangular stiffened plates. Part II: Localised blast loading.” Int. J. Impact Eng., 31(1), 85–111.
Lee, Y.-W., and Wierzbicki, T. (2005a). “Fracture prediction of thin plates under localised impulsive loading. Part I: Dishing.” Int. J. Impact Eng., 31(10), 1253–1276.
Lee, Y.-W., and Wierzbicki, T. (2005b). “Fracture prediction of thin plates under localised impulsive loading. Part II: Discing and petalling.” Int. J. Impact Eng., 31(10), 1277–1308.
Li, Q. M., and Huang, Y. G. (1989). “Dynamic plastic response of thin circular plates with transverse shear and rotatory inertia subjected to rectangular pulse loading.” Int. J. Impact Eng., 8(3), 219–228.
Li, Q. M., and Jones, N. (1994). “Blast loading of fully clamped circular plates with transverse shear effects.” Int. J. Solids Struct., 31(14), 1861–1876.
Li, Q. M., and Jones, N. (1995). “Blast loading of a “short” cylindrical shell with transverse shear effects.” Int. J. Impact Eng., 16(2), 331–353.
Li, Q. M., and Jones, N. (2000). “On dimensionless numbers for dynamic plastic response of structural members.” Arch. Appl. Mech., 70(4), 245–254.
Liu, J., and Jones, N. (1987). “Experimental investigation of clamped beams struck transversally by a mass.” Int. J. Impact Eng., 6(4), 303–335.
Micallef, K., Fallah, A. S., Pope, D. J., and Louca, L. A. (2012). “The dynamic performance of simply-supported rigid-plastic circular steel plates subjected to localised blast loading.” Int. J. Mech. Sci., 65(1), 177–191.
Neuberger, A., Peles, S., and Rittel, D. (2007a). “Scaling the response of circular plates subjected to large and close-range spherical explosions. Part I: Air-blast loading.” Int. J. Impact Eng., 34(5), 859–873.
Neuberger, A., Peles, S., and Rittel, D. (2007b). “Scaling the response of circular plates subjected to large and close-range spherical explosions. Part II: Buried charges.” Int. J. Impact Eng., 34(5), 874–882.
Nurick, G. N., Gelman, M. E., and Marshall, N. S. (1996). “Tearing of blast loaded plates with clamped boundary conditions.” Int. J. Impact Eng., 18(7–8), 803–827.
Nurick, G. N., and Martin, J. B. (1989a). “Deformation of thin plates subjected to impulsive loading–A review: Part I: Theoretical considerations.” Int. J. Impact Eng., 8(2), 159–170.
Nurick, G. N., and Martin, J. B. (1989b). “Deformation of thin plates subjected to impulsive loading–A review. Part II: Experimental studies.” Int. J. Impact Eng., 8(2), 171–186.
Nurick, G. N., and Shave, G. C. (1996). “The deformation and tearing of thin square plates subjected to impulsive loads: An experimental study.” Int. J. Impact Eng., 18(1), 99–116.
Onat, E. T., and Haythorntwaite, R. M. (1956). “The load-carrying capacity of circular plates at large deflection.” J. Appl. Mech., 23(1), 49–55.
Perrone, N. (1967). “Impulsively loaded strain-rate sensitive plates.” J. Appl. Mech., 34(2), 380–384.
Quanlin, J. (1988). “Dynamic response of an infinitely large rigid-plastic plate impacted by a rigid cylinder with transverse shear and rotatory inertia.” Int. J. Impact Eng., 7(4), 391–400.
Rajendran, R., and Lee, J. M. (2009). “Blast loaded plates.” Mar. Struct., 22(2), 99–127.
Ramu, S. A., and Iyengar, K. J. (1976). “Plastic response of orthotropic circular plates under blast loading.” Int. J. Solids Struct., 12(2), 125–133.
Sathyamoorthy, M. (1981). “Large amplitude vibration of circular plates including transverse shear and rotatory inertia.” Int. J. Solids Struct., 17(4), 443–449.
Sawczuk, A., and Duszek, M. (1963). “A note on the interaction of shear and bending in plastic plates.” Archives of Appl. Mech., 15(3), 411–426.
Shapiro, G. S. (1959). “On a rigid-plastic annular plate under impulse load.” J. Appl. Math. Mech., 23(1), 234–241.
Symonds, P. S. (1954). “Large plastic deformations of beams under blast loading.” Proc., 2nd U.S. National Congress of Applied Mechanics, ASME, New York, 505–515.
Symonds, P. S. (1980). “Finite elastic and plastic deformations of pulse loaded structures by an extended mode technique.” Int. J. Mech. Sci., 22(10), 597–605.
Symonds, P. S., and Chon, C. T. (1979). “Finite viscoplastic deflections of an impulsively loaded plate by the mode approximation technique.” J. Mech. Phys. Solids, 27(2), 115–133.
Symonds, P. S., and Wierzbicki, T. (1979). “Membrane mode solutions for impulsively loaded circular plates.” J. Appl. Mech., 46(1), 58–64.
Teeling-Smith, R. G., and Nurick, G. N. (1991). “The deformation and tearing of thin circular plates subjected to impulsive loads.” Int. J. Impact Eng., 11(1), 77–91.
Wang, A. J., and Hopkins, H. G. (1954). “On the plastic deformation of built-in circular plates under impulsive load.” J. Mech. Phys. Solids, 3(1), 22–37.
Wierzbicki, T. (1967). “Impulsive loading of rigid viscoplastic plates.” Int. J. Solids Struct., 3(4), 635–647.
Wierzbicki, T., and Florence, A. L. (1970). “A theoretical and experimental investigation of impulsively loaded clamped circular viscoplastic plates.” Int. J. Solids Struct., 6(5), 553–568.
Wierzbicki, T., and Nurick, G. N. (1996). “Large deformation of thin plates under localised impulsive loading.” Int. J. Impact Eng., 18(7–8), 899–918.
Zakrisson, B., Wikman, B., and Häggblad, H.-Å. (2011). “Numerical simulations of blast loads and structural deformation from near-field explosions in air.” Int. J. Impact Eng., 38(7), 597–612.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 140 • Issue 1 • January 2014
Pages: 159 - 171
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Oct 19, 2012
Accepted: Mar 25, 2013
Published online: Apr 1, 2013
Published in print: Jan 1, 2014
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.