A steady state formulation has been developed for thermal stress analysis. It uses features from both the Lagrangian formulation and the Eulerian formulation. The mesh sits on an Eulerian frame but deforms as if in the Lagrangian frame. Therefore, it is suitable for steady state problems with free boundaries. History dependent parameters are integrated along flow lines. A significant gain in computing speed and/or spatial resolution over transient analyses has been achieved together with a noticeable reduction for memory requirements. Numerical results are given for a three-dimensional analysis of edge weld.

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