A three-dimensional inverse problem for inhomogeneities in elastic solids

✍ Scribed by Bahir H. Eldiwany; Lewis T. Wheeler

• Publisher: Springer Netherlands
• Year: 1986
• Tongue: English
• Weight: 430 KB
• Volume: 16
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00043586

✦ Synopsis

The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnish the solution of this inverse problem. Exact and general expressions for the stress and displacement are given explicitly for points in the elastic matrix outside the inhomogeneity. The solution of the corresponding plane deformation problem is found as a limiting case. Several applications are presented, and results from the literature are confirmed as special cases. Finally, in equation (2.4), nj denote the components of the unit outward normal to OR. * We employ the usual conventions in connection with index notation: Latin letters have the range (1, 2, 3} and Greek letters, the range {1, 2}. Subscripts preceded by a comma indicate partial differentiation with respect to the corresponding cartesian coordinates.