Determination of welding residual stresses by inverse approach with eigenstrain formulations of BIE

Based on the concept of eigenstrain, a straightforward computational model of the inverse approach is proposed for determining the residual stress field induced by welding using the eigenstrain formulations of boundary integral equations (BIEs). The eigenstrains are approximately expressed in terms of low-order polynomials in the local area around welded zones. The domain integrals with polynomial eigenstrains are transformed into the boundary integrals to preserve the favourable features of the boundary-only discretization. The sensitivity matrices in the inverse approach for evaluating the eigenstrain fields are constructed by either the measured deformations on the boundary or the measured stresses in the domain after welding over selected measuring points, or by both the measured information. It shows from the numerical examples that the results of residual stresses from measured deformations are always better than those from measured stresses but they are sensitive to experimental noises. The results from stress measurements can be improved by introducing a few deformation measuring points while reducing the number of points for stress measuring to reduce the cost in practice.