Novosibirsk, Russia, May, 30 – June, 4, 2011

International Conference
"Modern Problems of Applied Mathematics and Mechanics: Theory, Experiment and Applications", devoted to the 90th anniversary of professor Nikolai N. Yanenko

Babakov V.  

The Problem about Resistant Force for a Circular Striker and Composite Target

     This paper considers low-speed penetration of an absolutely hard solid into a deformable obstruction (with a speed of encounter slower than the speed of sound in the obstruction) in which, unlike in high-speed collisions, the shape of the striker and the strength of the medium are essential. The study of the penetration process is a difficult mathematical problem, calling for the definition of an adequate mathematical model and, in most instances, computer calculations.
     It is proposed to use a known method of solving problems of plasticity theory which is based on one theorem of bound analysis - the theorem of upper bound of limit load. This method makes possible to obtain a quantitative solution, when the Saint-Venant model is used. This model supposes the material of the target to be incompressible and described by ideal plastic medium. The essence of this method is the use of the principal energy equality - equilibrium equation in the integral Lagrange form.
      A key aspect of the use of this equation is assignment of kinematical possible velocity fields. The specified velocity fields makes it possible to calculate the unknown vector of surfaces forces, the above theorem being used to estimate the upper bound of the actual load.
     The admissible velocity fields are assumed. The fields allow calculating all integrals analytically and getting a relatively simple calculation of the resistant force.

Abstracts file: babakov.doc
Full text file: Article.pdf

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