PSI- Issue 9

K. Sobianin et al. / Procedia Structural Integrity 9 (2018) 215–220 Author name / Structural Integrity Procedia 00 (2018) 000–000

218

4

deformed ball and gasket.

Table 1. The physical-mechanical properties of materials Material ρ, kg/m 3

E, GPa



reinforced concrete

2300 7800

30

0.2 0.3

steel (metal reinforcement, striker)

200

gasket

950

0.2 – 200

0.42

With the finite-element method, the finite-element algebraic analog of the variation equation (1) relative to the unknown nodal values takes the form     0      M U t K U t , (2) where M, К are the mass and stiffness matrices, U(t) is the vector of the unknown nodal variables as a function of time t, and    U t is the vector of nodal accelerations. The external effect was determined by the initial conditions for velocity and displacement vectors. For the reinforced concrete beam and gasket, these conditions were assumed to be equal to zero. At the initial moment of the ball impact on the gasket, all its points had the velocity equal to V 0 and directed to the normal of the gasket surface, and the displacement vector components were equal to zero. The convergence and reliability of the obtained solutions were evaluated by analyzing the rate of fulfillment of natural boundary conditions and the character of convergence of numerical solutions depending on the degree of finite element discretization of the examined domains. 3. Results of numerical simulation The developed algorithm for solving the problem of dynamic interaction between the elements of the "striker - gasket - reinforced concrete beam" systemwas used to implement a series of numerical experiments. The main purpose of these experiments is to determine the dependence of impulse duration τ (Fig. 1b) on a variety of factors: mass, radius and initial velocity of the striker, as well as elasticity modulus and thickness of the gasket. These five parameters were chosen because of the fact that they can be used to effectively control the magnitude of the impulse duration. At the first stage of numerical experiments, the results obtained from the solution of the problem in the three dimensional formulation (taking into account the metal reinforcement) and in the axisymmetric formulation (without considering the reinforcement) were compared. It was found that consideration of the reinforcement has a minor effect on the impulse duration  . Therefore, all subsequent calculations were carried out in the axisymmetric formulation, which is less time-consuming for obtaining a numerical solution. Fig. 3 shows the plots of the force impulse duration as a function of five parameters mentioned above. The plots were constructed for parameters that varied within the following limits: mass from 0.05 kg. to 10 kg; radius of the striker from 5 mm to 140 mm, the velocity of the striker from 0.05 m/s to 10 m/s; modulus of elasticity of the gasket from 0.2 GPa to 200 GPa; the thickness of the gasket from 0.1 mm to 50 mm. It should be noted that for all curves presented in the figure one of the five specified parameters was allowed to vary within the specified limits, and the remaining four corresponded to the reference values: the striker mass was 4 kg, the striker radius was 4 mm, the striker velocity was 1 m/s, the modulus of the gasket was 10 9 Pa, the thickness of the gasket was 2mm. At these values of the parameters, the calculated impulse duration was 1.04   ms (this value was marked by a dot on the curves in Fig. 3).