PSI - Issue 13

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

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inspected structure. This procedure is implemented as follows. The local impulse force excited by the striker impact is applied to some points at the reinforced concrete structure. The mechanical response of the structure is recorded by a set of sensors (accelerometers, velocimeters, etc.) located at different parts of the structure. Then the response recorded immediately after installation of a monitoring system is compared with current records. Comparison makes it possible to assess the degree of accumulation of irreversible defects and the changes in the properties of the structure material. The objective of this study is the identification of parameters of the local impulse force, which excites mechanical vibrations of the desired spectrum in the structure, and generates an elastic wave, which have necessary characteristics of the front. One of the main parameters of the impulse action that determine these characteristics is the duration of the impulse action. Therefore, an analysis of the dependence of the impulse duration on various factors and the evaluation of the possibility of controlling such force impulses is the focus of this study. Here, within the framework of the theory of elasticity, the results of the solution of the initial-boundary problem on the dynamic interaction of the

elements of the "striker-gasket-reinforced concrete beam" system are analyzed. 2. Mathematical formulation of the problem and its numerical implementation

The mechanical aspects of the problem studying the interactions between a striker, a gasket and a reinforced concrete beam are schematically represented in Fig.1a. In the experiment, the fixed reinforced concrete beam interacted through the elastic gasket with the flying metal ball, which at the initial moment of its contact with the gasket had the velocity equal to V 0 and directed along the normal to the gasket surface. The contact interaction between the ball and the gasket gave rise to the force impulse, which initiated the shock-wave process in the reinforced concrete beam. The characteristic force impulse - time curve is given in Fig.1b.

b

a

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: (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. ij    ij i i   i V S V i dV p u U d u S d V         ,