Numerical Solution Of The Problem Of The Influence Of A Plane Nonstationary Elastic Wave On Cylindrical Bodies (original) (raw)

In this paper the effect of a nonstationary wave on cylindrical bodies with circular and rectangular cross sections is considered. The problem is solved in a flat setting, by a numerical method (FEM). Numerical results were obtained under the influence of the load by the single functions of Heuside. Introduction and statement of the problem. For modern engineering practice, the construction of underground structures is very important and important role is played by research and analysis of wave phenomena occurring in media with various inhomogeneities. The results obtained in this field are decisive for the development of methods for calculating the dynamic effects on structures and structures interacting with various types of ground media. However, in solving the problem posed, it is impossible to achieve significant progress without a deep theoretical analysis of them. The main provisions of the dynamic theory of seismic stability (DTS) are developed in the works [1,2,3] and others. These provisions are as follows [5, 6], a subterranean network of an arbitrary circuit is considered, consisting of elastic rods (pipelines, tunnel trunks) and high rigidity matching structures (observation wells, metro stations, etc.). The movement of the soil surrounding the pipeline during earthquakes is represented as a traveling wave of variable intensity. With this formulation of the problem, only the process associated with the oscillations of the pipeline in the ground is considered, without taking into account the volume of the oscillating soil mass [7]. This takes into account the ground support, friction slipping of the rods in the ground. In this formulation, the problem is solved with the help of a set of differential equations describing the vibrations of the rods, taking into account the dynamic and kinematic conditions for the coupling of the rods. Based on the calculation model described above, the effect of seismic waves on pipelines experiencing longitudinal oscillations has been investigated [8,9]. Among the most commonly used computed methods used in the calculation of underground pipelines, tunnel structures are the finite element method and grids. Variational-difference methods include the Bubnov-Galerkin method, the Ritz method, and the finite element method [10, 11]. Let us dwell on the latter, which has now found wide application for solving practical engineering problems. During the calculations, the calculation area was unevenly divided into rectangular and triangular finite elements. This breakdown was condensed as it approached the ground zone adjacent to the pipe. At present, there are well-developed software complexes for solving planar and spatial problems of linear and nonlinear theory of elasticity according to FEM [7,8,9,10,12,13]. Such problems can be solved on a multiply connected domain of any shape (the exception is the definition of a stress-strain state in a small neighborhood of a singular point). In a rectangular Cartesian coordinate system, a plane region in which a free circular (or square) hole is defined is considered. We consider reinforcement with a ratio of the diameter of the middle contour to the thickness, equal to ten. Before the start of the moment of rotation t = 0, the points of the considered mechanical system are at rest: