Solving the non-linear system
The finite element method – material nonlinear analysis
Article REF: C6004 V1
Solving the non-linear system
The finite element method – material nonlinear analysis

Author : Alaa CHATEAUNEUF

Publication date: May 10, 2018 | Lire en français

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5. Solving the non-linear system

The resolution of elastoplastic problems must satisfy, on the one hand, the overall balance between applied external forces and internal forces in the structure and, on the other hand, compliance with elastoplastic flow rules leading to a redistribution of internal stresses in the structure.

It is therefore necessary to carry out an incremental analysis, since the state of the structure depends on the loading history and the initial state of the structure.

5.1 Structural resolution: Newton-Raphson method

In order to follow the loading trajectory, the total load {F} is decomposed into a number of increments {ΔF}, small enough to ensure convergence (figure

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