NONDESTRUCTIVE DETECTION OF CAVITIES BY AN INVERSE ELASTOSTATICS BOUNDARY-ELEMENT METHOD

The elastostatics boundary element method is applied in an inverse pro blem approach to the nondestructive detection of subsurface cavities i n structures. The boundary conditions at the exposed surface are overs pecified: tractions are specified and displacements are used as additi onal 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 co ordinates of the interior nodes to be fixed thus reducing the number o f unknowns at each cavity node to one. The initial guess will not corr espond to the actual cavity, consequently, the BEM solution will yield displacements which do not agree with the reference displacements. Th is leads to residuals at each node. The cavity is then located by iter atively driving these residuals to zero. Newton's method and the steep est descent method are considered in this effort. Iterative updates of the cavity geometry are kept within a physically realistic feasible r egion. Validation cases are presented for the detection of single circ ular and elliptic holes located at various positions within a rectangu lar plate. Numerical results demonstrate the successful detection of s ubsurface cavities by this method. Finally, results are presented for an experiment in which the surface displacements are determined by a l aser speckle photography technique. A centrally located circular hole is successfully located using these surface displacement data.