Abstract
A simplified analysis is carried out to derive the analytical solution for the large deflection of a fully clamped metal sandwich beam under impulsive loading. Using the classical yield criterion for sandwich structures, the moment–axial force interaction induced by large deflection is uncoupled. Then, plastic bending and stretching deformations are separated into two distinct phases, i.e., a bending-only phase and a plastic string phase. The simplified analytical solutions for the maximum deflection and structural response time have been obtained and are in good agreement with the previous theoretical and numerical results. Moreover, the analytical formulae are employed to determine the optimal geometries of a sandwich beam that maximize the resistance to impulsive loading at a given mass.
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Qiu X.M., Yu T.X.: Some topics in recent advances and applications of structural impact dynamics. Appl. Mech. Rev. 64, 03801 (2011)
Ashby M.F., Evans A.G., Fleck N.A., Gibson A.G., Hutchinson J.W., Wadley H.N.G.: Metal Foams: A Design Guide. Butterworth-Heinemann, Oxford (2000)
Gibson A.G., Ashby M.F.: Cellular solids: Structure and properties, 2nd edn. Cambridge University Press, Cambridge (1997)
Xue Z., Hutchinson J.W.: A comparative study of blast-resistant metal sandwich plates. Int. J. Impact Eng. 30, 1283–1305 (2004)
Xue Z., Hutchinson J.W.: Preliminary assessment of sandwich plates subject to blast loading. Int. J. Mech. Sci. 45, 687–705 (2003)
Radford D.D., Fleck N.A., Deshpande V.S.: The response of clamped sandwich beams subjected to shock loading. Int. J. Impact Eng. 32, 968–987 (2006)
Rubino V., Deshpande V.S., Fleck N.A.: The dynamic response of end-clamped sandwich beams with a Y-frame or corrugated core. Int. J. Impact Eng. 35, 829–844 (2008)
Wang Z., Jing L., Ning J., Zhao L.: The structural response of clamped sandwich beams subjected to impact loading. Compos. Struct. 93, 1300–1308 (2011)
Rathbun H.J., Radford D.D., Xue Z., He M.Y., Yang J., Deshpande V.S. et al.: Performance of metallic honeycomb-core sandwich beams under shock loading. Int. J. Solids Struct. 43, 1746–1763 (2006)
Fleck N.A., Deshpande V.S.: The resistance of clamped sandwich beams to shock loading. J. Appl. Mech. 71, 386–401 (2004)
Qiu X., Deshpande V.S., Fleck N.A.: Finite element analysis of the dynamic response of clamped sandwich beams subject to shock loading. Eur. J. Mech. A Solids 22, 801–814 (2003)
Qiu X., Deshpande V.S., Fleck N.A.: Dynamic response of a clamped circular sandwich plate subject to shock loading. J. App. Mech. 71, 637–645 (2004)
Qiu X., Deshpande V.S., Fleck N.A.: Impulsive loading of clamped monolithic and sandwich beams over a central patch. J. Mech. Phys. solids 53, 1015–1046 (2005)
Zhu F., Wang Z., Lu G., Nurick G.: Some theoretical considerations on the dynamic response of sandwich structures under impulsive loading. Int. J. Impact Eng. 37, 625–637 (2010)
Zhu F., Zhao L., Lu G., Wang Z.: Deformation and failure of blast-loaded metallic sandwich panels—experimental investigations. Int. J. Impact Eng. 35, 937–951 (2008)
Cui X., Zhao L., Wang Z., Zhao H., Fang D.: A lattice deformation based model of metallic lattice sandwich plates subjected to impulsive loading. Int. J. Solids Struct. 49, 2854–2862 (2012)
Cui X., Zhao L., Wang Z., Zhao H., Fang D.: Dynamic response of metallic lattice sandwich structures to impulsive loading. Int. J. Impact Eng. 43, 1–5 (2012)
Qin Q.H., Wang T.J.: An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch. Compos. Struct. 88, 509–518 (2009)
Qin Q., Wang M., Wang Z., Zhang J., Wang T.J.: A yield criterion and plastic analysis for physically asymmetric sandwich beam with metal foam core. Int. J. Appl. Mech. 05, 1350037 (2013)
Qin Q., Zhang J., Wang Z., Wang T.J.: Large deflection of geometrically asymmetric metal foam core sandwich beam transversely loaded by a flat punch. Int. J. Aerosp. Lightweight Struct. 1, 23–46 (2011)
Wang Z., Qin Q., Zhang J., Wang T.J.: Low-velocity impact response of geometrically asymmetric slender sandwich beams with metal foam core. Compos. Struct. 98, 1–14 (2013)
Qin Q., Wang T.J.: A theoretical analysis of the dynamic response of metallic sandwich beam under impulsive loading. Eur. J. Mech. A Solids 28, 1014–1025 (2009)
Qin Q., Wang T.J., Zhao S.: Large deflections of metallic sandwich and monolithic beams under locally impulsive loading. Int. J. Mech. Sci. 51, 752–773 (2009)
Yu T.X., Stronge W.J.: Large deflections of a rigid-plastic beam on foundation from impact. Int. J. Impact Eng. 9, 115–126 (1990)
Qin, Q., Wang, T.J.: Impulsive loading of a fully clamped circular metallic foam core sandwich plate. In: Proceedings of the 7th International Conference on Shock and Impact Loads on Structures, pp. 481–488. Beijing (2007)
Jones N.: Structural Impact, 2nd edn. Cambridge University Press, New York (2012)
Martin J.B.: Plasticity: Fundamentals and General Results. MIT Press, Cambridge (1975)
Symonds P.S., Jones N.: Impulsive loading of fully clamped beams with finite plastic deflections and strain-rate sensitivity. Int. J. Mech. Sci. 14, 49–69 (1972)
Schubak R., Anderson D., Olson M.: Simplified dynamic analysis of rigid-plastic beams. Int. J. Impact Eng. 8, 27–42 (1989)
Symmonds, P.S.: Large plastic deformations of beams under blast type loading. In: Proceedings of the Second US National Congress of Applied Mechanics, pp. 505–515. (1954)
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Yuan, C., Qin, Q. & Wang, T.J. Simplified analysis of large deflection response of a metal sandwich beam subjected to impulsive loading. Acta Mech 226, 3639–3651 (2015). https://doi.org/10.1007/s00707-015-1405-4
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DOI: https://doi.org/10.1007/s00707-015-1405-4