The wave field in a rectangular area with discontinuities in boundary conditions

Subject	Computational methods in partial differential equations
Title	The wave field in a rectangular area with discontinuities in boundary conditions
Author(s)	Nurgali Ashirbayev, Azimkhan Abzhapbarov, Zhazira Alibekova
Keywords	dynamic loading, plane deformation, singular point, elastic
Abstract	In this study we consider the plane elastic isotropic medium with a rectangular cross section of finite size. At the initial time on a certain part of the front of the rectangular field of applied external dynamic П - shaped loading and the remainder of this boundary is stress-free. On the other side of the rectangular area defined boundary conditions. As plane strain conditions, the problem is solved numerically by using the spatial characteristics [1-2]. Especially considering the body is that the singular points of the rectangular area of the front boundary conditions discontinuity of the first kind. Namely, in these critical points are obtained allowing the system of equations for the unknown functions. By numerical implementation established the stability calculation algorithms for a sufficiently long time. Results of the study in its final form brought to the numerical solution.

Influence of heterogeneity of the character fixing the border

Subject	Computational methods in partial differential equations
Title	Influence of heterogeneity of the character fixing the border
Author(s)	Nurgali Ashirbayev, Raina Bekmoldayeva, Zhansaya Ashirbayeva, Shadiyar Altynbekov
Keywords	isotropic medium, plane strain, a singular point, wave processes, numerical algorithm
Abstract	In this study was considered planar elastic isotropic medium with rectangular cross section of finite size. At the initial time on the front border of the rectangular area impinges absolute rigid body having speed. Lateral sides of the rectangular area are free from stress. On the lower boundary are given inhomogeneous boundary conditions. In conditions when the plane deformation problem has been solved numerically using the method spatial characteristics [1-4]. We have developed a numerical algorithm for the calculation of stress and displacement velocity at points of discontinuity of the boundary conditions that are special because of the abrupt change in the boundary conditions. Results of the study in its final form brought to the numerical solution.