Mechanics Based Design of Structures and Machines, 34: 139–156, 2006 Copyright © Taylor & Francis Group, LLC Modeling of High-Speed Penetration Into Concrete Shields and Shape Optimization of Impactors # G. Ben-Dor, A. Dubinsky, and T. Elperin Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel Abstract: We modified the model of Forrestal and Tzou (1997) for a case of an arbitrary impactor having a shape of a body of revolution with a plane bluntness and derived a formula for the depth of penetration (DOP) into semi- infinite concrete shield. The shape of the impactor that attains the maximum DOP for a given impact velocity is found through analytical investigation of a corresponding non-classical variational problem when the criterion of optimization is a function of integral functionals of the unknown solution. It is shown that the optimum shape is close to a blunt cone. The influence of the penetration model parameters on the optimum solution is studied. Keywords: Concrete; Impact; Modeling; Optimization; Penetration. INTRODUCTION The two-stage two-term model suggested by Forrestal et al. (1994) for modeling penetration of ogive-shaped projectiles into concrete semi- infinite shields attracted interest of the researchers in the field and initiated a number of studies associated with selecting parameters of the model, generalization of the model to arbitrary bodies of revolution including projectiles with plane bluntness, to shields with a finite Received August 29, 2005; Accepted February 27, 2006 # Communicated by N. Banichuk. Correspondence: T. Elperin, Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel; E-mail: elperin@.bgu.ac.il