Non linear problems: Introduction

ABSTRACT

Solid mechanics problems in general, and specifically in the case of geomaterials, are very often significantly non linear. Although linear numerical models may be used as rough approximations to the problem solution, non linearities are very often too significant to be neglected. To solve these problems special non linear strategies are necessary. A series of non linear analysis techniques are presented in the context of the finite element method. These techniques are based on the Newton-Raphson method, a very well known mot finding algorithm. The different techniques presented are: full Newton-Raphson with load control, modified Newton-Raphson, quasi Newton methods and Newton-Rahson with displacement control. Implementation of the Newton-Raphson method in a finite element program is also covered.

KEYWORDS:

• Non linear problem
• finite element method