Elastoplastic analysis using an arc-length method and quasi-Newton iterations : Some related problems
The set of non-linear equations occurring in the step-by-step solution of quasi-static elastoplastic problems is usually solved using iterative techniques such as the Quasi-Newton (QN) or the Secant Newton (SN) techniques. In order to deal with failures of these methods in certain circumstances, continuation methods, such as the Arc-Length (AL) method, were introduced. This paper discusses how the QN/SN techniques may be combined with the AL method in the indirect method of solution. Two specific methods are used: the (unsymmetric) Broyden update and the BFGS update. The Broyden update is left formally unchanged, upgrading from standard to arc-length control, whereas the BFGS update needs to be more deeply corrected. The Broyden method is used as a reference method in order to study the impact of the correction on the BFGS formula. An homogeneous test and the notched bar test of Marques are used as an illustration.
Bibliographic Reference: Paper presented: Conférence Européenne sur les Nouvelles Avancées en Calcul des Structures, Giens (FR), April 2-5, 1991
Availability: Available from (1) as Paper EN 35964 ORA
Record Number: 199110374 / Last updated on: 1994-12-02
Original language: en
Available languages: en