On the generalized plane strain problem in thermoelasticity

The reliability of the solutions of problems of two-dimensional linear elasticity is examined in relation to the solutions of the corresponding three-dimensional problems. It is shown that the solution of a long cylindrical body with free ends can be approximated by the classical plane strain solution plus a correction which is the solution of another two-dimensional problem. The corrected solution is exponentially accurate sufficiently far from the ends. In the vicinity of the free ends a three-dimensional model has to be used.