Multi-level substructuring and an experimental self-adaptive newton-raphson method for two-dimensional nonlinear analysis

The substructuring technique has been employed in structural analysis for 25 years. Until now, the use of this technique in nonlinear analysis has been limited to localized situations. Moreover, the benefit in calculation time one can obtain is restricted to the amount of 50%. However, as will be described in this paper, a new scheme of multi-level substructuring technique in nonlinear analysis has been developed. With this scheme an efficiency of 75–85% has been reached and a connection level higher than three can easily be expanded. The Newton-Raphson method and its modified version are the most well known algorithms in nonlinear numerical analysis. The former has, nevertheless, the severe disadvantage of reforming the stiffness matrix at every iteration and, in fact, some of the stages are not necessary. The latter has also the disadvantage of a slow convergence, as the recalculation of the stiffness matrix is executed in certain fixed iterations. Thus, to overcome the difficulties mentioned above, an experimental self-adaptive Newton-Raphson algorithm, which offers an automatic decision as to whether the stiffness matrix is reformed or not, is introduced. In applying this algorithm a saving of 30–50% in execution time can be achieved. Combining these two new schemes in 2-D nonlinear analysis, a dramatic effort of 85–90% is yielded. A typical flow chart and two numerical examples are also presented.