On the interior stress problem for elastic bodies

The classic Sherman-Lauricella integral equation and an integral equation d ue to Muskhelishvili for the interior stress problem are modified. The modi fied formulations differ from the classic ones in several respects: Both mo difications are based on uniqueness conditions with clear physical interpre tations and, more importantly, they do not require the arbitrary placement of a paint inside the computational domain. Furthermore, in the modified Mu skhelishvili equation the unknown quantity, which is solved for, is simply related to the stress. In Muskhelishvili's origional formulation the unknow n quantity is related to the displacement. Numerical examples demonstrate t he greater stability of the modified schemes. [S0021-8936(00)01304-0].