# Nonlinear Analysis Control

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.

Note

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

From the Main Menu select Analysis >  Analysis Control > Nonlinear.

Nonlinear Type

Select a type of nonlinear analysis

Geometry Nonlinear: Geometric large displacement nonlinear analysis

Material Nonlinear: Material plasticity static analysis

Note 1

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

 Element Geometry Nonlinear Geometry Nonlinear         (Initial Force for Geometric Stiffness) Material Nonlinear Truss O O O Tension only O O O Hook O O O Cable O O Δ Compression only O O O Gap O O O Beam O O Δ Plate - Thick O Δ O Plate - Thin O (Considered as Thick Plate) Δ O (Considered as Thick Plate) Plane Stress O Δ O Plane Strain X Δ O Axisymmetry X Δ O Solid O Δ O

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

Note 2

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

 Limitation Geometry Nonlinear Material Nonlinear Material + Geometry Nonlinear Remark Beam End Release O x x Plate End Release O x x Pretension Load O x x Prestress Load O x x Initial Forces for Geometric Stiffness O x x Temperature Loads O x x Material=SRC x x x

Note 3

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

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

Maximum number of iterations of analysis per Load Step.

If Arc-Length is selected

Number of Increment 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

Note

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.

Note
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 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.

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

Data for Newton-Raphson/Arch-Length/Displacement-Control Method
Title of Iteration Method specified

Step: Number of Load Steps entered

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 button.

Note 1

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.

Note 2

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.