Nondestructive Detection Of Cavities By An Inverse Elastostatics Boundary-Element Method
Abbreviated Journal Title
Eng. Anal. Bound. Elem.
BOUNDARY ELEMENTS METHOD; ELASTOSTATICS; INVERSE PROBLEMS; NONDESTRUCTIVE EVALUATION; LASER SPECKLE PHOTOGRAPHY; Engineering, Multidisciplinary; Mathematics, Interdisciplinary; Applications
The elastostatics boundary element method is applied in an inverse problem approach to the nondestructive detection of subsurface cavities in structures. The boundary conditions at the exposed surface are overspecified: tractions are specified and displacements are used as additional data for solving the inverse problem. In the developed iterative procedure, an initial guess is made for the shape of the cavity and a grid pattern is laid out. The use of this pattern allows one of the coordinates of the interior nodes to be fixed thus reducing the number of unknowns at each cavity node to one. The initial guess will not correspond to the actual cavity, consequently, the BEM solution will yield displacements which do not agree with the reference displacements. This leads to residuals at each node. The cavity is then located by iteratively driving these residuals to zero. Newton's method and the steepest descent method are considered in this effort. Iterative updates of the cavity geometry are kept within a physically realistic feasible region. Validation cases are presented for the detection of single circular and elliptic holes located at various positions within a rectangular plate. Numerical results demonstrate the successful detection of subsurface cavities by this method. Finally, results are presented for an experiment in which the surface displacements are determined by a laser speckle photography technique. A centrally located circular hole is successfully located using these surface displacement data.
Engineering Analysis with Boundary Elements
"Nondestructive Detection Of Cavities By An Inverse Elastostatics Boundary-Element Method" (1994). Faculty Bibliography 1990s. 1082.