A dual orthogonality procedure for non-linear finite element equations Original Research Article

In the orthogonal residual procedure for solution of non-linear finite element equations, the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is shown here that the quasi-Newton formulation of the orthogonal residual method consists of a simple one-term correction of the displacement subincrement, and that this correction leads to orthogonality between the corrected displacement subincrement and the current increment of the internal force vector, thus defining a dual orthogonality algorithm. It is demonstrated how the algorithm can be implemented to combine a single update of the stiffness matrix for each load increment in normal circumstances with full updates locally if increasing stiffness is encountered. The algorithm is illustrated by examples.