PSI - Issue 13

I.N. Shardakov et al. / Procedia Structural Integrity 13 (2018) 1362–1366 Author name / Structural Integrity Procedia 00 (2018) 000–000

1364

3

a

b

Fig.2. Finite-element images of the striker-gasket- reinforced concrete beam system in three-dimensional (a) and axisymmetric (b) cases

The finite-element meshes were inhomogeneous, which made it possible to get the best approximated solution in the domains where the stress and strain gradients could reach the maximum values. In the solution of this problem, the non-stationary dynamic contact between the striker (in the form of a ball) and the gasket was considered. The selected types of finite elements allowed us to take into account changes in the contact surface area between the 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" system was 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.