Optimum Shape of High Speed Impactor for Concrete Targets Using PSOA Heuristic

Francesco Ragnedda, Mauro Serra
DOI: 10.4236/eng.2010.24035                

Abstract

The present paper deals with the optimum shape design of an absolutely rigid impactor which penetrates into a semi-infinite concrete shield. The objective function to maximize is the depth of penetration (DOP for short) of the impactor; in the case of impactors with axisymmetric shapes DOP is calculated using formulas obtained by Ben-Dor et al. [1-3] with the method of local variations [4] and based on the mechanical model proposed by Forrestal and Tzou [5]. In the present paper we show that using a different class of admissible functions, more general than the axisymmetric one, better results can be obtained. To solve the formulated optimization problem we used a custom version of the particle swarm optimization method (briefly denoted by PSOA), a very recent numerical optimization algorithm of guided random global search. Numerical results show the optimal shape for various types of shields and corresponding DOP; some Ben-Dor et al. [1-3] results are compared to solutions obtained.

Keywords

Impactor; Optimization; Particle swarm; Global Search

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. Ben-Dor, A. Dubinsky and T. Elperin, “Numerical Solutions for Shape Optimization of an Impactor Penetrating into a Semi-infinite Target,” Computers and Structures, Vol. 81, No. 1, 2003, pp. 9-14.
[2]	G. Ben-Dor, A. Dubinsky, T. Elperin, “Shape Optimization of an Impactor Penetrating into a Concrete or a Limestone Target,” International Journal of Solids and Structures, Vol. 40, No. 17, 2003, pp. 4487-4500.
[3]	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, Vol. 34, No. 2, 2006, pp. 139-156.
[4]	N. V. Banichuk, V. M. Petrov and F. L. Chernousko, “The Method of Local Variations for Variational Problems Involving Non-additive Functionals,” USSR Computational Mathematics and Mathematical Physics, Vol. 9, No. 3, 1969, pp. 66-76.
[5]	M. J. Forrestal and D. Y. Tzou, “A Spherical Cavity-expansion Penetration Model for Concrete Targets,” International Journal of Solids and Structures, Vol. 34, No. 31-32, 1997, pp. 4127-4146.
[6]	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,” International Journal of Impact Engineering, Vol. 15, No. 4, 1994, pp. 396-405.
[7]	M. J. Forrestal, D. J. Frew, S. J. Hanchak and S. Brar, “Penetration of Grout and Concrete Targets with Ogive- nose Steel Projectiles,” International Journal of Impact Engineering, Vol. 18, No. 5, 1996, pp. 465-476.
[8]	G. Ben-Dor, A. Dubinsky and T. Elperin, “Applied High- speed Plate Penetration Dynamics,” Springer, Berlin, 2006.
[9]	A. I. Bunimovich and G. E. Yakunina, “On the Shape of Minimum-resistance Solids of Revolution Moving in Plastically Compressible and Elastic-Plastic Media,” Jour- nal of Applied Mathematics and Mechanics, Vol. 51, No. 2, 1987, pp. 386-392.
[10]	N. A. Ostapenko and G. E. Yakunina, “The Shape of Slender Three Dimensional Bodies with Maximum Depth of Penetration into Dense Media,” Journal of Applied Mathematics and Mechanics, Vol. 63, 1999, pp. 953-967.
[11]	G. E. Yakunina, “On Body Shapes Providing Maximum Penetration Depth in Dense Media,” Doklady Physics, Vol. 46, No. 2, 2001, pp. 140-143.
[12]	G. E. Yakunina, “On the Optimal Shapes of Bodies Moving in Dense Media,” Doklady Physics, Vol. 50, No. 12, 2005, pp. 650-654.
[13]	N. V. Banichuk and S. Y. Ivanova, “Shape Optimization of Rigid 3-D High-speed Impactor Penetrating into Concrete Shields,” Mechanics Based Design of Structures and Machines, Vol. 36, 2008, pp. 249-259.
[14]	D. Bucur and G. Buttazzo, “Variational Methods in Shape Optimization Problems,” Birkhauser, Boston, 2005.
[15]	R. C. Eberhart and J. Kennedy, “A New Optimizer Using Particle Swarm Theory,” Proceedings of the 6th International Symposium on Micromachine and Human Science, Nagoya, 1995, pp. 39-43.
[16]	J. Kennedy and R. C. Eberhart, “Particle Swarm Optimization,” Proceedings of the IEEE International Joint Conference on Neural Networks, Perth, 1995, pp. 1942-1948.
[17]	M. Clerc, “Particle swarm optimization,” ISTE, London, 2006.
[18]	M. M. Ali and P. Kaelo, “Improved particle swarm algorithms for global optimization,” Applied Mathematics and Computation, Vol. 196, 2008, pp. 578-593.
[19]	P. C. Fourie and A. A. Groenwold, “The Particle Swarm Optimization Algorithm in Size and Shape Optimization,” Structural and Multidisciplinary Optimization, Vol. 23, No. 4, 2002, pp. 259-267.
[20]	A. P. Engelbrecht, “Fundamentals of computational swarm intelligence,” Wiley, Chichester, 2005.