Newton-Raphson method

The algorithm is based on Newton-Raphson method for solution of non-linear problems. The method is robust for most of problems. It may, however, fail in the vicinity of inflection points of loading diagram. This may occur for example at compressed 1D members subject to small eccentricity or to small transverse load. Except for the mentioned example, the method can be applied for wide range of problems. It provides for solution of extremely large deformations.

The load acting on the structure can be divided into several steps. The default number of steps is eight. If this number is not sufficient, the program issues a warning.

The rotation achieved in one increment should not exceed 5°.

The accuracy of the method can be increased through refinement of the finite element mesh or by the increase in total number of increments. For example, the solution of a single beam divided to a single finite element will not give sufficient results.

In some specific cases, high number of increments may solve even problems that tend to a singular solution which is typical for the analysis of post-critical states.

Note : This method requires that a 1D member is divided to at least four (4) finite elements. Usually, such division is adjusted automatically whenever Newton-Raphson method is selected for calculation.

 

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