Cluster modeling of the interaction of statyonary SH-waves with a system of curvilinear cracks in a half-space

Abstract

A method is proposed for solving problems of mathematical physics for semi-infinite media containing systems of curvilinear cuts. Based on singular integral equations (SIE), a unified approach to solving the problem has been developed. Numerical implementation was carried out using parallelisation. A graph of the duration of the initial cluster hour is given for calculating an array of searched functions in the context of a parabolic form as a function of the number of processes for one variant of implementation. It is shown that the entire algorithm scales well and has an efficient number of processes. The expected result was obtained, because the structure of the calculation process in models based on SIE is mostly unchanged and built on well-defined procedures. It turned out that 150–200 processes are effective. An accuracy of 10–12 was achieved with the number of collocation points of the contour of each section N = 300, because the algorithm for numerical solution of the problem uses interpolation by Chebyshev polynomials in accordance with the fact that the unknown function has a key feature at the ends of the section, which causes a higher speed of convergence of the algorithm. The study of the question of the further increase in the accuracy of the result was not conducted. The corresponding dynamic boundary value problems for a restrained and force-free half-plane are studied. The influence of the curvature of defects, their interaction and proximity of the boundary on the magnitude and nature of the change in the dynamic stress intensity coefficients was studied. To check the reliability of the algorithm, two tests were carried out: removing three inhomogeneities at a distance of 106 of their length from each other and saturating the system by increasing the number of geometrically equal reflectors to 13–15. When removed, the characteristics of each reflector tend to the characteristics of a single one, and when saturated, they tend to the results of the corresponding periodic problem. The agreement between the results showed good reliability of the algorithm. The proposed method can be used to assess the influence of various mechanical or geometric factors on the strength of bodies with defects.