PSI- Issue 9

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

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(a)

(b)

Fig.1. (a) Calculation scheme of the problem; (b) the force impulse curve

Mathematical modeling is performed based on the principle of virtual displacements (Lurie, A.I., 2005), which takes into account the variation of the work of internal stresses, surface forces and inertia forces:

ij    



i  

ij (1) where σ ii , ε ii are the components of elastic stress and strain tensors, u i are the components of the displacement vector, u i  are the components of the acceleration vector, p i are the components of the surface force vector, ρ is density, V is the volume, S σ is the surface under the action of the components of the surface force vector. A numerical solution to the variational equation (1) has been carried out by the finite element method using the ANSYS software. Finite-element images were constructed by means of finite elements with a quadratic approximation of displacement vector components, including elements that take into account contact interactions. The problem of striker-gasket-beam dynamic interactions was solved in three-dimensional and axisymmetric formulations (axial symmetry with respect to the longitudinal axis of the beam). In the three-dimensional case, we considered the influence of a metal reinforcement on the force impulse duration in the case of contact interaction of the striker with the gasket; in the axisymmetric case, this factor was ignored. The finite-element images of the striker gasket-beam system constructed for three-dimensional and axisymmetric cases are presented in Figs. 2a, b. i i V S V i dV p u U d u S d V       ,

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