When treating nonlinear problems with the Finite Element formulation, the need to solve nonlinear sets of equations arises. Classically, those nonlinear sets of equations were solved by performing an incremental / iterative analysis with a full Newton-Raphson method.

Today, one can chose from a wide range of methods. The modifications to the original fNR method use tangent stiffness matrices, which are updated at most once per increment. Quasi-Newton methods use secant matrices instead of tangent matrices. Secant-Newton methods are simplifications of the Quasi-Newton.

This work deals, in particular, with the implementation of these methods in an object-oriented code and with the comparison between them on several tests. The expected behavior of the methods is observed from the results. Also, an acceleration line-search technique is implemented to improve the results supplied by the previous methods.

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Published on 29/01/19
Submitted on 29/01/19

Licence: CC BY-NC-SA license

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