Classical elasticity problems prescribe traction or displacement data on the entire boundary. The Almansi boundary value problem prescribes both traction and displacement data on a boundary subset, on its complement nothing (traction nor displacement ) is prescribed. In 1907, for isotropic elastic solids E. Almansi proved that for such non-classical problems solutions could only conditionally exist. However, if the solution exists then it is unique. Following his analytical continuation reasoning the same can be proved for anisotropic solids.
In designing finite element procedures to capture unbounded (infinite) domains, as in soil-structure interaction problems, the cloning algorithm complies with the restrictions imposed by Almansi type ill-posed problems.
Both the theoretical development and numerical implementation will be presented.
Update : December 20, 2017