NON-ELEMENT MODELING OF DOMAINS WITH DEFECTS AND IDENTIFICATION OF THEIR SHAPE IN PROBLEMS DEFINED BY NAVIER-LAME EQUATION

摘要

The paper presents an original method to identify the shape of defects with smooth boundary in domains defined by Navier-Lame. For this purpose the previously obtained parametric integral equation system (PIES) was generalized. In the PIES the boundary shape is mathematically defined in the continuous way by means of Bezier, B-spline, etc. curves. In order to define it only small number of points from external and internal boundary of considered domain is posed. The identification of the smooth boundary is reduced to the identification of de Boor control points. Finally the solution of the problem is reduced to the solution of nonlinear system of algebraic equations. Coordinates of identified control points (which describe the shape of the defect) are obtained after solving the system of equations.