 # Iteration

### Glossary Term

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Iteration is a repetitive process that approaches a goal. In numerical structural analysis, this method is generally used to find a solution to a problem with nonlinear relation. Such a problem usually consists of an equation with nonlinear terms that depend on a variable.

In the first step, the iteration process uses an arbitrary start value for the unknown variable and solves the terms on the left and the right side of the equation. If the equation is not fulfilled, the process repeats with a modified start value. This iterative process continues until the equation is fulfilled. In this case, we talk about convergence and the last used variable value is the solution.

The accuracy of this procedure depends on the variables used. This means that it is usually necessary to perform a lot of iteration steps to find the exact solution. If a solution with the reduced accuracy is sufficient, the convergence of the iteration is related to a tolerance criterion. In this case, a new iteration is only started if the difference between the terms of the left and the right side of the equation is greater than the defined tolerance criterion.

#### Iterative Processes in Structural Analysis

• Determination of internal forces on a deformed system (second-order analysis)
• Simulation of nonlinear material properties (plasticity)
• Determination of contact stresses between two bodies positively connected to each other

#### Iteration in RFEM and RSTAB

In RFEM and RSTAB, the criteria and maximum iterations for nonlinear calculations are organized under 'Calculation' → 'Calculation Parameters' in the 'Global Calculation Parameters' tab.