An inverse formulation with boundary elements
Abstract
A mathematical formulation for the solution of inverse problems pertaining to the identification of flaw shapes and the reconstruction of boundary conditions in a continua is described. Integral relationships are derived for the variation of field variables with respect to variation in flaw shape using Taylor series expansions. Similar relationships for the variation of boundary conditions with variation in flaw shape are also obtained. These variations allow the development of an iterative framework to advance an initially assumed flaw shape toward its actual configuration. The iterations are based upon and are driven by the difference in the values of computed response for the assumed flaw shape from their experimentally measured values at specified locations. The resulting equations are cast into the matrix form for solution using the boundary element method.
 Publication:

ASME Journal of Applied Mechanics
 Pub Date:
 December 1992
 Bibcode:
 1992ATJAM..59..835Z
 Keywords:

 Boundary Element Method;
 Boundary Integral Method;
 Crack Geometry;
 Inverse Scattering;
 Potential Gradients;
 Taylor Series;
 Boundary Conditions;
 Iteration;
 Matrices (Mathematics);
 Nondestructive Tests;
 Structural Mechanics