## Function

- Specify the iteration method and convergence conditions for performing a nonlinear analysis reflecting large displacement and material nonlinear analysis. The large displacement analysis can be applied to both general static analysis and construction stage analysis.
- Material nonlinear analysis can only be applied to static analysis.
- Prior to an analysis, specify the sequence of applying loads in Loading Sequence for Nonlinear Analysis, and define the convergence criteria for nonlinear analysis in Nonlinear Analysis Control. Specified loading sequence is effective only when Newton-Raphson is selected as the Iteration Method. Large displacement analysis and material nonlinear analysis can be performed on Truss, Plate, Plane Stress, Plane Strain, Axisymmetric, and Solid elements.

Tension-only/Compression-only element will be changed to Truss element in Eigenvalue Analysis.

## Call

From the main menu, select **[Analysis] tab > [Analysis Control] group > [Nonlinear]**

## Input

Nonlinear Analysis Control dialog box

### Nonlinear Type

Select a type of nonlinear analysis.

**Geometry Nonlinear** : Geometric large displacement nonlinear analysis

**Material Nonlinear** : Material plasticity static analysis

Following elements can be used in geometry nonlinear analysis and/or material nonlinear analysis.

(O : Analysis can be performed. / X : Analysis cannot be performed. / △ : Corresponding elements are considered as linear elements and then analysis can be performed.)

Geometry nonlinear analysis and/or material nonlinear analysis cannot be performed for the items marked x.

In case of Beam End Release and Plate End Release, the material nonlinear analysis cannot be performed for the following case:

1. When Load > Nonlinear Analysis > Loading Sequence for Nonlinear Analysis is used.

2. When "Include Nonlinear Analysis-Accumulative Stage" option is selected in Analysis > Construction Stage Analysis Control

Analysis result is produced only at both I & J ends of elements in geometry nonlinear analysis.

### Iteration Method

Select the method of iteration.

**If Newton-Raphson is selected**

**Number of Load Steps** : Divide the total load into the number of Load Steps and apply the loads by each step.

**Maximum Number of Iterations/Load Step** : Maximum number of iterations of analysis per Load Step.

**If Arc-Length is selected**

**Number of Increment Steps** : The maximum number of incremental steps.

**Maximum Number of Iterations/Increment Step** : Maximum number of iterations of analysis per Increment Step.

**Initial Force Ratio for Unit Arc-Length(%)** : Ratio of the Initial Force per Unit Arc-Length

Real number (decimal) can be input.

**Maximum Displacement Boundary** : Magnitude of maximum displacement

**If Displacement-Control is selected**

**Number of Displacement Steps** : Divide the total displacement into the number of Displacement Steps and apply the incremental displacement by each step.

**Maximum Number of Iterations/Increment Step** : Maximum number of iterations of analysis per Increment Step

**Master Node** : A reference node for displacement control

**Direction** : Direction of the displacement control

**Maximum Displacement** : The magnitude of maximum displacement to be applied to analysis

### Convergence Criteria

Specify the basis on which to assess the convergence.

**Energy Norm** : Assess the convergence on the basis of Energy (Member force x displacement) Norm.

**Displacement Norm** : Assess the convergence on the basis of Displacement.

**Force Norm** : Assess the convergence on the basis of Member Force Norm.

The selection of the convergence criteria for repeating or ending the analysis must be based on the condition to reflect the effects of various degrees of freedom. For example, in the case of Displacement Norm, if the displacement resulting from the corresponding analysis step is {D1}, and the total displacement accumulated from each step is {D2}, the Norm is expressed as . If this value is smaller than the specified value, a convergence is considered to have occurred and the program stops the iterative analysis.

**Remove Nonlinear Analysis Control Data** : Remove the conditions for a nonlinear analysis.

### Load Case Specific Nonlinear Analysis Control Data

The above defined Iteration Method is applied individually by load cases. If the same iteration method is applied to all the load cases, this dialog box need not be used. The above defined Iteration Method is applied individually by load cases. If the same iteration method is applied to all the load cases, this dialog box need not be used.

Load Case Specific Nonlinear Analysis Control Data dialog box

**Iteration Method**Specify between Newton-Raphson and Displacement-Control.

**Data for Newton-Rapson/Arch-Length/Displacement-Control Method**

Title of Iteration Method specified

**Step** : Number of Load Steps entered

**Load Factor** : Load factors for each increment

8 steps are generated in the Dialog box above in accordance with the Number of Load Steps entered.

Load Factors can be user-difined, or auto-generated by clicking on the **Generate Default Load Factor** button.

When Arc-Length Method (ALM) is used to solve the nonlinear equilibrium equation, a real number can be inputted into the "Initial Force Ratio for Unit Arc-Length (%)" text box in Nonlinear Analysis Control.

** **In nonlinear analysis, the sequence of applying loads can be defined in Loading Sequence for Nonlinear Analysis. Loading sequence can be used when Newton-Raphson and Displacement-Control are selected as Iteration Method. In one model, both Displacement-Control and Newton-Raphson iteration method can be used. However, the load case specified as Newton-Raphson iteration method must be applied in advance of the load case specifined as Displacement-Control method.