Nonlinear finite element techniques using and object-oriented code

Abstract

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.