Determining the Unknown Traction of a Cracked Elastic Body Using the Inverse Technique with the Dual Boundary Element Method

Abstract: The two-dimensional elasticity problem of an isotropic material, containing a centered-crack with unknown boundary traction is studied by the inverse pro-cedure. The dual boundary integral equations are used to analyze the problem. While solving the ill-posed inverse problem, both of the conjugate gradient method and the regularization method are used. A scaling factor depend-ing upon the material constant µ is introduced into the sensitivity matrix in order to keep the order of magni-tude the same throughout the formulation. The result by using the displacement measurement will be compared with those by stress measurement, and an extensive dis-cussion will be given. Finally, the effect of measurement error to the inverse problem is also discussed