A Dual Orthogonality Procedure for Nonlinear Finite Element Equations

In the orthogonal residual procedure for solution of nonlinear finite element equations the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is here shown 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.