Deformation Transverse Shear Bending State of a Thin Plate Layer of an Anisotropic Geological Medium From the Action of Concentrated Energy Impulses

Abstract

A method is proposed for study the structural stability of the deformation state of structural blocks of the earth's crust, approximated in the form of plate layers of the geological medium when transverse shear bending from the action of concentrated energy impulses. Advances here are carried out in the two directions. First, in contrast to the previous article, the physical and mechanical model of the geological medium is endowed with anisotropic properties, which makes it possible to increase the adequacy of the obtained numerical results to the specifics of the real problem. Secondly, instead of the simplest bilinear 4-node finite elements, the special spectral non-algebraic 8-node finite iso-parametric finite elements are used, the use of which significantly increases both the accuracy of calculations and their reliability in the sense of ensuring the robustness of calculations for relatively small values of the plate thickness. It should be noted that the Finite Element Method uses exclusively only algebraic finite elements (power polynomials in the h-version and orthogonal polynomials in the p-version). It is known from approximation theory that the use of spectral non-algebraic approximations improves the quality of approximations. Therefore, their introduction into the structure of finite element calculations can improve the quality of modeling in the study of the strain-stress-state (SSS) of the geological medium. A structural block (SB) is understood as a plate layer with plan dimensions exceeding the thickness by more than 10 times. The identification of hazardous zones in the rock massive due to stress concentration is complemented by the development of mechanical, mathematical and computational tools for modeling the curvature of the earth's crust during bending based on the classical theory of Kirchhoff and refined Reissner-Mindlin theory. Test calculations have shown that the accuracy of the calculation and the quality of geometric modeling of fragments of an anisotropic geological environment based on the refined 8-node spectral finite element is significantly better than for the 8-node algebraic finite