Physical Non-Linear Analysis Using the Finite Element Method One- Dimensional by Iterative Potra-Pták Method

Resumo

In recent years, structural analysis has has gained a notoriety due to the technological advance. The
structures that require a non-linear analysis, require the execution of a large number of calculations, with large
and sparse matrices, requiring the use of iterative methods to solve the problems. This context, there is a need to
search for more efficient solution methods or those that are adapted to the needs of advances in Civil
Engineering analysis. Within the process of structural analysis, different analyzes have to be done in order to
achieve structural security. Physical non-linear analysis considers a non-linear constitutive relationship, which
when added to the analysis of the structure increases the use of the resistant capacity of the materials, in addition
to making it more realistic. Currently, frameworks are used in many practical engineering applications from
simple to more complex structures. Increasing the resistant capacity of these new materials can produce more
economical structures. Structures that have plastic behavior only after the yelding was modeled using a
parameter for hardening module. The current work aim is compare the solution methods Newton-Raphson,
Modified Newton-Raphson and Potra-Pták. To analyses the performance of the methods, frameworks problems
with physical non-linearity are analyzed by algorithms using Finite Element Methods developed in Fortran90.
The both Newton-Raphson methods are largely used in non-linear analysis and have quadratics convergence and
the Potra-Pták is a new method that has cubic convergence. According with the result, the Potra-Pták method
become an advantageous comparing to others iterative methods.