On Mathematical Models of the Dynamics of Three-Dimensional Elastic Bodies. Part 2. Bodies with Discretely Observable Initial Boundary Condition

Abstract

Based on the integral representation of solutions of differential mathematical models of the stable dynamics of spatially unlimited elastic medium in the Lame form an integral mathematical model of the initial boundary problem of the dynamics of an elastic body of arbitrary geometric configuration with arbitrary initial boundary conditions is constructed. The cases of both the spatial unlimited body and time interval, on which its dynamics is modeled, are considered. The constructed mathematical models, exactly satisfying classical mathematical models of three-dimensional theory of elasticity, according to the root mean square criterion, are agreed with the observations of its initial boundary state. The root mean square accuracy of modeling the initial boundary observations of a modeled object is estimated. These observations are defined in discretely determined surface-time points. The uniqueness conditions of researched mathematical modeling are also given in this paper.