Enhanced solution control for physically and geometrically non-linear problems. I: The subplane control approach. II: Comparative performance analysis.

*(English)*Zbl 0957.74034From the summary: Geometrically or physically nonlinear problems are often characterized by the presence of critical points with snapping behaviour in the structural response. These structural or material instabilities usually lead to inefficiency of standard numerical solution techniques. Special numerical procedures are therefore required to pass critical points. This paper presents a solution technique which is based on a constraint equation that is defined on a subplane of the degree-of-freedom hyperspace or a hyperspace constructed from specific functions of the degrees of freedom. This unified approach includes many existing methods which have been proposed by various authors. Part I fully elaborates the proposed solution strategy, including a fully automatic load control, i.e. load estimation, adaptation and correction. Part II presents a comparative analysis in which several choices for the control function in the subplane method are confronted with classical update algorithms.

##### MSC:

74M05 | Control, switches and devices (“smart materials”) in solid mechanics |

74K99 | Thin bodies, structures |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

##### Keywords:

subplane of degree-of-freedom hyperspace; local subplane method; weighted subplane method; path following technique; arc-length control; critical points; constraint equation; fully automatic load control; load estimation
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\textit{M. G. D. Geers}, Int. J. Numer. Methods Eng. 46, No. 2, 177--230 (1999; Zbl 0957.74034)

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