Geometrical Non-linear Analysis in Advance Design

written by Achraf Ben Afia

GRAITEC Advance Design (AD) offers solutions for geometrical non-linear structural behavior and contact non-linearity. This blog focuses on explaining the modeling and analysis procedure for structures with geometrical non-linearity, using the P-Delta effect as an illustration.

There are three main sources of non-linear structural behavior:

• Geometrical non-linearity (large displacements/strains, buckling, etc)
• Material non-linearity (plasticity, cracking, creep, etc)
• Contact non-linearity (change of support conditions during motion, etc)

Fortunately for Graitec clients, AD provides solutions for geometrical and contact non-linearity problems.

The aim of this blog is to explain the procedure to model and analyze a structure with a geometrical non-linearity. P-Delta effect is a good illustration of geometrical non-linearity.

Following is an example of a steel column subjected to a load in X and Z direction (vertical direction).

1.  First, we define a column with a fixed support.

2. We apply a point load; in this example we apply Fx=10 kN and FZ=-200 kN.

3. Then, right clicking on “settings” in project browser, we select “Non-linear Static”.

   

 

4. We select NL in the project browser and enable large displacement.

Note: There are two options for non-linear calculation: load increments or displacement increments. Following is an explanation about both methods:

Load increments method: A Newton Raphson force control solver, in which the applied loads to the structure are divided into equal force increments. In each analysis step, an additional force increment is introduced, and the structure is analyzed nonlinearly.

Displacement increments method: In this approach, loads are applied to the structure, and a target displacement is set for a chosen control node. This target displacement is divided into equal displacement increments. At each analysis step, the nonlinear solver adjusts the scaling of all applied loads to achieve the required displacement increment at the chosen control node.

 

For this example, we will select load increments and make sure that “large deformation” is checked.

5.  Next, we click on Analysis options and add analysis by selecting load or combination case.

 

6. After clicking Ok, we will get a dialog box containing parameters related to nonlinear analysis. These parameters are grouped into five families:

Load case or combination

• Identifier – name: displays the name of the case used in the non-linear analysis.
• Coefficient: defines the scale coefficient for each case.

Incrementation

• Number: the number of analysis steps.

Note: The time duration of the non-linear analysis directly depends on the number of steps. Therefore, start by introducing smaller values for this parameter. If the analysis does not converge within the initial number of steps, re-run the analysis after increasing this number of saved steps.

• Iterations by step controls the number of iterations per step. The default value of 50 is suitable for most cases.
• Stabilize iterations: iterations are stabilized up to this iteration number (in each step).

Save results

• Frequency/step: the rate of the results is saved per step. By default, the results are saved only once (in their final state). We can modify this to “complete” in order to visualize results for every step.

Update stiffness

• Mode: defines the method for updating the stiffness matrix:  i.e., complete (default), quasi-Newton, or none.
• Period: defines the update rate: by iteration inside each step, for the complete update mode or by step, for the quasi-Newton update mode.

Convergence

• The solver iterates to achieve equilibrium at each step of the analysis. Equilibrium is achieved when the magnitude of the force error is smaller than the convergence tolerance. The convergence tolerance for energy, force and displacement can be viewed or modified.

 

For this example, we will consider the default parameters.

7.  We click Ok and run the FE analysis.

Comparing simple static analysis with nonlinear analysis, we can clearly see the difference.

– Displacement: 29.8 cm for static vs. 224.5 cm for non-linear analysis.

– Moment My: 80 kN.m for static vs. 518.4 kN.m for non-linear analysis.

In fact, the displacement and internal forces are larger when we perform a nonlinear analysis, because the load is applied in the deformed shape after every increment.

     

   

 

Conclusion

In conclusion, AD offers solutions for geometrical non-linear structural behavior and contact non-linearity. This blog demonstrates the steps involved in setting up the non-linear static analysis, including selecting the suitable method and enabling large deformation. Both load increment and displacement increment methods are ready to be employed in AD. Overall, geometrical non-linear analysis in AD is valuable for understanding complex structural behavior and overcoming the limitations of linear analysis.

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If you’re interested in learning more about GRAITEC Advance Design, contact Graitec Group today and talk to an industry expert.

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