Framework analysis of the object domain of stationary dynamic problems of the elasticity theory for isotropic media with arbitrary discontinuities

Abstract

A general scheme of framework analysis of an object domain is considered. The domain involves a wide class of problems of the theory of dynamic elasticity, which allows one to develop a software tool for the synthesis of applications (a CASE method) of parallel high-precision numerical solution of this class of problems. This article proposes a scheme of parallel high-precision solution to systems of singular integral equations that occur in the analysis of certain problems of diffraction of elastic harmonic waves on systems of discontinuities of an arbitrary cross-section. New computational results are presented.Keywords: relational framework, relational database schema, object domain, dynamic problem of elasticity theory, isotropic medium with arbitrary discontinuities, CASE tool.

High-Precision Maximum Stresses in the Problem of Interaction of Elastic Waves with a System of Cylindrical Cavities Under Plane Strain

“…As the numerical analysis has shown, in case of action from infinity of P-and SV-waves the saturation effect [9] is also observed in the described system; however, not strictly (as well as in [5,10]). And although no more than 20 reflectors are enough for the averaged analysis in case of linear and symmetric (with respect to the load) arrangement of geometrically identical holes, minor pulsations are observed if their number increases.…”

“…As well as in [3][4][5][6], formula (12) corresponds to the rule of approximate calculation of regular integrals (11). Therefore, in the numerical implementation of singular integrals, the Hilbert kernel was not selected.…”

“…In the numerical implementation, the algorithm was parallelized [7] by the scheme from [5]. The accuracy of computations was checked by comparing the results for different values of N. For the majority of problems of this class, 1000 points of collocation of the contour are enough to calculate contour stresses with accuracy 10 8 -.…”

“…We used the fact that with grid saturation, the stress-strain state of the system under study tends to a similar state in periodic case [5,9], and in the present study we compared the obtained results with those presented in [11] for the case of periodic system of elliptic holes. Comparison with the results from [11] has also shown good reliability of the used computing schemes.…”

“…In [3], integral representations are constructed for elastic potentials in terms of which components of displacement vector and stress tensor are expressed. In the present paper, we will develop the technique proposed in [4,5], where the main characteristics of the stress-strain state is displacement vector.…”