Enhanced solution control for physically and geometrically non-linear problems. Part I – The subplane control approach

Solution control techniques or so-called path following techniques alleviate the numerical analyses of engineering problems considerably. While being indispensable for the passage of limit points on the so-lution path, they also permit to set up a fully automatic load incrementation procedure. The performance of a path following technique depends on the quality of the applied load estimation, adaptation and correction scheme. The second part of this two-part series of papers analyses dierent path following strategies with respect to their numerical eciency. Examples are given in geometrically and physically non-linear analysis and an overall comparison is made between a number of subplane approaches which have been presented in Part I, as well as some classical arc-length procedures. Various choices for the control function are scruti-nized. The eciency and the applicability of the subplane control approach is illustrated and its superiority with respect to classical approaches is emphasized. Comments and recommendations on the choice of the control functions are given. Copyright? 1999 John Wiley & Sons, Ltd. KEY WORDS: automated solution control; arc-length control; subplane method; geometrically and physically non-linear analyses 1