Abstract
We consider the problem of penetration of rigid pyramidal bodies (impactors) into a strained medium in the case of large speeds of penetration and estimate the depth of the impactor penetration. To this end, we use the two-stage penetration model proposed by Forrestall. We state the shape optimization problem for the penetrating body, which is based on the consideration of a set of bodies of pyramidal external shape with given fixed mass. We study both solid and hollow (shell-shaped) bodies. For the optimization functional we take the penetration depth of the penetrating body, and for the projection variable we take the number of faces of the pyramidal body. We present the results of computations of the penetration depth for different shapes of the impactor and show that, both for shells and solid impactors, the bodies of the shape of a circular cone are optimal. The problems of high-speed penetration of rigid bodies into a deformable medium are nowadays very topical problems [1] which have been studied by Russian and foreign authors [2–8].
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References
D. M. Klimov, “Mechanics is the Basis of Engineering and Rational Nature Management,” Vestnik RAS 77(5), 452–459 (2007) [Herald Russ. Acad. Sci. (Engl. Transl.) 77 (3), 292–298 (2007)].
A. I. Bunimovich and G. E. Yakunina, “On the Shape of Minimum-Resistance Solids of Revolution Moving in Plastically Compressible and Elastic-Plastic Media,” Prikl. Mat. Mekh. 51(3), 496–503 (1987) [J. Appl. Math. Mech. (Engl. Transl.) 51 (3), 386–392 (1987)].
G. E. Yakunina, “On the Optimal Shapes of Bodies Moving in Dense Media,” Dokl. Akad. Nauk 405(4), 484–488 (2005) [Dokl. Phys. (Engl. Transl.) 50 (12), 650–654 (2005)].
M. J. Forrestal and D. Y. Tzou, “A Spherical Cavity-Expansion Penetration Model for Concrete Targets,” Intern. J. Solids and Structures 34(31–32), 4127–4146 (1997).
M. J. Forrestal, B. S. Altman, J. D. Cargile, and S. J. Hanchak, “An Empirical Equation for Penetration Depth of Ogive-Nose Projectiles into Concrete Targets,” Intern. J. Impact Eng. 15(4), 395–405 (1994).
G. Ben-Dor, A. Dubinsky, and T. Elperin, “Numerical Solution for Shape Optimization of Impactor Penetrating into a Semi-Infinite Target,” Computers and Structure 81(1), 9–14 (2003).
G. Ben-Dor, A. Dubinsky, and T. Elperin, “Shape Optimization of an Impactor Penetrating into a Concrete or a Limestone Target,” Intern. J. Solids and Structures 40(17), 4487–4500 (2003).
G. Ben-Dor, A. Dubinsky, and T. Elperin, “Modeling of High-Speed Penetration into Concrete Shields and Shape Optimization of Impactors,” Mechanics Based Design of Structures and Machines 34(2), 139–156 (2006).
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Original Russian Text © N.V. Banichuk, S.Yu. Ivanova, E.V. Makeev, 2008, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2008, No. 4, pp. 176–183.
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Banichuk, N.V., Ivanova, S.Y. & Makeev, E.V. On the penetration of nonaxisymmetric bodies into a deformable solid medium and their shape optimization. Mech. Solids 43, 671–677 (2008). https://doi.org/10.3103/S0025654408040158
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DOI: https://doi.org/10.3103/S0025654408040158