Study of the blow evenly stretched plate lying on the base

Examines the impact of a massive body at evenly stretched (compressed) plate, lying on the ground. The total displacement of the plate is considered elastic, and local to the contact is elastic-plastic. Considered a common approach in the analysis of the attack on the center of a rectangular or circular plate lying on the base of the Winkler or an endless plate on the surface of an ideal incompressible fluid. When calculating the main characteristics of the impact (force of contact interaction, its maximum, the moment of achievement, duration of impact, coefficient of restitution at impact) important is the consideration of the initial impact velocity, the magnitude of the external influences on the body and the plate, the state of material bodies. the analysis of the dynamic function of the influence of the «plate – base». The collision is considered in the framework of the theory of S. P. Timoshenko, which neglect wave processes in a small area of contact. The solution of the quasistatic contact problems for elastoplastic bodies, which are in good agreement with numerical and empirical results. For large local plastic deformations can be neglected elasticity of the material in the contact area, use the solution to rigid-plastic contact problem and to investigate rigid-plastic collision. The asymptotic results are in good agreement with analytical and numerical solutions to the problem of hitting the half-space and an endless plate and can be recommended for engineering calculations.