#simcenter

Quick Overview

It is often required to create lightweight, simplified versions of large FEMs in order to reduce solution time or post-processing effort. A common simplification technique that can be used with relatively slender parts is midsurfacing. Whereas plate theory can accurately predict the stiffness of each part, there can be uncertainty at the structural connections  be they welded, bonded or fastened- due to the idealization of the part thickness and the creation of non-manifold joints.

Simcenter FE Model Correlation and FE Model Update allow you to compare the modal properties of fine and simplified FEMs, as well as to automatically update the simplified FEM to minimize the differences. In this example, we’ll take a relatively large FEM of a cone with 2 welded flanges as reference, and update a simplified, midsurfaced version of the FEM so that the modal frequencies agree well. The simplified model will provide the work solution. We’ll also create the 2 FEMs.

Core content

Create Reference FEM

Starting with the CAD geometry, we first create the larger reference FEM and SIM, using NX Nastran as solver:

Set the Solution Type to SOL 103 Real Eigenvalues

Create a parabolic tetrahedral mesh of the part using the default size computed by Simcenter:

As material, select Aluminum_6061 from the Simcenter materials library

Make the SIM the work part, select the 2 bottom faces of the flanges to define fixed constraints:

Solve the normal modes Solution. 10 modes are computed, the first being at 1318 Hz.

Create Work FEM

Go back to the part file in the modeling application.  Create a new NX Nastran FEM and SIM, and set the Solution Type to SOL 200 Model Update

Using the Simulation File View, navigate to the idealized part.

Create an associative copy of the CAD part using WAVE linking. Do not hide the original part.

Click Midsurface by Face Pairs

Select the solid body and click Automatically Create Face Pairs. The midsurfaced part looks like this

Create 4 datum planes, one on each vertical face of the 2 flanges

Divide the cone sheet body faces using the datum planes to create 4 new faces around the flange joints. The meshes on these faces will be assigned a material property which will be used by FE Model Update.

Return to the fem. Hide the original polygon geometry, keeping the newly created sheet bodies. Use Merge Faces to get rid of the unneeded divisions on the top of the cone

Use Automatic Stitch Edge to merge the coincident edges of the flanges and the cone. Create 3 different 2D meshes and place them in the following collectors:

1- A collector for the general cone section

2- A collector for the joint section which will be optimized.

3- Finally, a collector for the flanges

Shift-Select the 3 meshes in the sim navigator, Edit Mesh Associated Data,

And set the thickness source to Midsurface. Select the general cone section collector, Edit the PSHELL1 property and select Aluminum_6061 as material. Select the flange collector, and assign PSHELL1 to it. Then select the joint section collector, Edit the PSHELL2 property, and assign to it a copy of Aluminum_6061 which you rename OPTIM.

Go the SIM.

Create a new Material Design Variable

Select OPTIM and its field E (Modulus) as design variable.

Create fixed constraints at the base of the 2 flanges

Edit the solution. In the Bulk Data tab, Create Design Variables

Add to the active list the variable you just created. Set the Model Reduction method to Modal, and create a New DOF set

Select all the nodes in the FEM, and check DOFs 1, 2 and 3

Solve the solution. Note the first mode is at 1053 Hz.

Correlate Work and Reference Models

In the Correlation tab, create a New Analysis Reference Solution.

Select the .op2 file from the SOL 103 solution using the reference FEM.

In the Correlation tab, create a New Correlation and select the Work and Reference solutions

Select the Mode Pairs node in the SIM navigator, open the Correlation Details View, and notice there are significant frequency errors between both models. However the mode shapes correlate very well, as indicated by the high MAC value for each mode pair.

Model Update

We will now optimize the work model to improve the correlation with the reference model. Create a New Model Update

Select the same solutions as for the Correlation. Notice the single design variable is displayed with an initial, normalized value of 1

In the Model Update group of the Correlation tab, click Optimize

Since we’re not concerned about limiting the change in the design variable, set the Overall Design Variable Weight to 1%

The optimization ends with the design variable reaching its default upper limit of 2:

Comparing Current and Initial frequency errors, we notice an improvement, which is not as significant as expected because of the limit on the design variable.

We can edit the design variable’s Upper Bound and set it to 4

After optimization, we notice a much better correlation

The JOINT design variable’s normalized value is now 3.

This means the Young’s Modulus of the OPTIM material has tripled, which is a substantial change. Since SOL 200 Model Update Solution returns first-order sensitivities which are valid for small changes, the solution needs to be updated. In the Model Update group of the Correlation tab, click Update Finite Element Model. This command automatically updates the material and physical properties in the FEM.

The new value of E for material OPTIM is 2.07 X108 kPa, from the original value of 6.98 X107 kPa

Re-solve the SOL 200 Model Update solution, Reset the Design Variable to 1 using the Reset command and Refresh the Model Update. We notice that the frequency errors are different than after the previous optimization, this is because of the linear sensitivities:

Optimize once again

Let’s now Update the FEM. The new value of E is 4.14 X108 kPa.

Re-solve the SOL 200 Solution and Refresh the Model Update. The frequency error for the first mode pair is less than 1%, it was originally around 20%. Side-by-side mode shape displays complement the Correlation Details View.

All MAC values are above 0.96. The largest frequency difference is for mode 9, 7.7%. It was originally around 15%

By changing the optimizer settings, it’s possible to reduce the maximum error for all 10 modes to less than 5%, however this results in an increase in the error for mode 1, which may be the most important mode due to its effective mass.  The maximum error can also be reduced by further splitting the faces of the work model and creating more design variables.

Summary

Quick Overview

A powerful way of reducing design conservatism is to validate the finite element model used to simulate its performance. Comparing the simulation model’s natural frequencies and mode shapes with those acquired in test generates confidence in the model’s ability to represent the as-built structure. This in turn allows analysts to reduce the safety factors used to compute structural margins of safety. Simcenter 3D FE Model Correlation supports both test and simulation engineers who wish to perform such a comparison, efficiently providing both visual and quantitative feedback. 

Background

The Modal Assurance Criterion (MAC) is a parameter indicating the degree of consistency between a mode shape from test and another one from simulation. This parameter is a scalar value between 0 and 1: A MAC value near 1 indicates a high degree of correlation or consistency between two mode shapes.

Suppose {ΨA} and {ΨX} are two mode shapes that you want to compare: Their MAC is expressed as follows:

Where:

N is the number of common simulation and test mode shape components

The superscript * indicates the complex conjugate value.

There are LA x LX MAC numbers for given mode shape matrices [ΨA] and [ΨX], where LA is the number of mode shapes in [ΨA] and LX is the number of mode shapes in [ΨX]. These are presented in matrix format:

Problem Definition

We wish to compare the natural frequencies and mode shapes of an aircraft engine nacelle finite element model with the equivalent data acquired during a modal test of the actual structure:

The model and test article both represent half the nacelle.

1. Normal Modes Solution

First we create an NX Nastran normal modes solution, requesting the first 20 free-free (unconstrained) modes of the FEM. The first 6 modes describe rigid body motion, in which the structure moves without any internal strain. The next 14 modes are elastic modes, which are the ones we are interested in correlating.

In the simulation navigator, select the top-most sim node and right-click New Solution

The Solution dialog pops up. Enter a Name and as Solution Type, select Sol 103 Real Eigenvalues from the list

In the Case Control tab of the Solution dialog, next to Lanczos data click Create Modeling Object

  In the Real Eigenvalues  Lanczos dialog, enter 20 as the Number of Desired Modes. Click OK twice.

In the sim navigator, select the solution, right-click, Solve

After the solution is complete, the mode shapes can be displayed from the post navigator.

2. Import Test Geometry and Results

In the Correlation tab of the Simcenter 3D ribbon, click New Test Reference Solution

Set the Solution Type to Modal Test Data, and then select a Geometry File which contains the test geometry (test sensors, coordinate systems and traces) as well as a Modes File containing the test mode shapes and natural frequencies. In this case, the same file contains both the geometry and the mode shapes.

Click OK.  There are now 2 solutions in the sim file.

Since Solution 1 is active and points to imported geometry, the fem is now displayed as monotonic grey.

3. Align the Test Model

In the sim navigator, under Solution 1, select the Test Model node, and right-click Show Model.

You can also click Show Sensors, to see the individual sensors as triads.

It is clear that the test model and the FEM do not share the same global coordinate system. The test model will have to be aligned with the FEM in order for correlation to be possible.

In the sim navigator, under Solution 1, select the Test Model node, and right-click Alignment. The Alignment Control dialog will appear, allowing you to choose 3 test nodes and the equivalent 3 nodes in the FEM. Checking on Preview allows you to see the cumulative effect of the pairs you have selected.

You may need to repeat this step if it is not clear which test sensors correspond to which nodes. After you have successfully performed the alignment, you may select Fine Tune Alignment to further nudge the test model by specifying discrete translations and rotations.

4. Create a Correlation

In the Correlation tab of the Simcenter 3D ribbon, click New Correlation

The Correlation dialog appears. Select test Solution 1 as the Reference Solution, and your normal modes solution as the Work Solution

By default, low-frequency (rigid-body) modes are filtered out. In the Node Map Settings group, enter 75 mm as the matching tolerance between the test sensors and the FEM nodes.  Click OK.

Based on the alignment that was performed, and the tolerance entered in the last step, Simcenter FE Model Correlation was able to map 51 sensors to the FE model nodes, based on proximity. If you repeat the alignment and choose different alignment node pairs, you will see a different number of paired nodes in brackets. The test and analysis mode shapes will be interrogated at these 51 locations to determine the MAC.

Next, select the Mode Pairing node under Correlation 1, right-click Edit. The default mode pairing criterion is MAC with a minimum value of 0.7: This means that test and analysis modes having the greatest MAC value above 0.7 will be paired, others will not be paired. For example, work (analysis) mode 12 is not paired to any test mode.

Other pairing methods can be selected.

Next, select the Mode Pairs (n) node under the Mode Pairing node and click the Correlation Details View bar

This pops up the Correlation Details View, which shows the test (reference) and analysis (work) frequencies, percent frequency error and MAC, for each mode pair.

Select any mode pair row in the table, right-click Side-by-Side Animation:

This will bring up a synchronized 2-view layout, showing the test and analysis mode shape animation

Select the Correlation Metrics node under Correlation 1, right-click Correlate. In the Correlate dialog, click Show Results Heat Map

The heat map display shows the MAC matrix

In the Correlate dialog, click Show Results Spreadsheet

SC FE Model Correlation will send the MAC matrix to an Excel spreadsheet.

Select the Correlation Metrics node under Correlation 1, right-click Generate 1-COMAC Results.

This will show sensors at which the individual MAC components are poorest.

Quick Overview

Simcenter offers a dedicated application to map steady state or transient flow results onto a target model, typically an independent structural model from the same geometry but with a different mesh. For example, one could be interested in the stress and distortion analysis of a canopy due to wind forces.

The target FEM must use the same global coordinate system as the source FEM, and both models should be geometrically congruent. However, they need not share the same mesh. Results are mapped from the selected solution on the source model, to a solution on the target model, based on proximity and with optional zone associations. The output of the mapping solution can then be used by the target solution.

In what follows, we describe how to create an NX Nastran structural analysis using forces that are mapped from a Simcenter Thermal/Flow analysis.

Workflow overview

The main steps are:

Create a part file containing the structure and air volume.

Create a Simcenter Thermal/Flow fem file with only the air volume meshed.

Create a new Simulation containing a Thermal/Flow Solution with Flow Analysis.

Run the Thermal/Flow Solution.

Back to the part file; create a NX Nastran fem file of the structure.

Create a new Simulation containing a Thermal/Flow Solution with Mapping Analysis.

Specify the mapping target area then Solve.

Assign the structural boundary conditions and solve the structural analysis.

For more information, see Simcenter Thermal/Flow, Electronic Systems Cooling, and Space Systems Thermal documentation.

Create the Thermal/Flow Simulation

1.     Create the part

We begin by creating the part file, as shown in Figure 1. This represents a simple tubular structure submitted to lateral winds.

Figure 1: Part file containing both structure and fluid volume

2.     Create the Thermal/Flow FEM

Next, create the fem file. In the “Edit FEM” window, make sure to choose Simcenter Thermal/Flow (Flow) as the “Solver Environment”, as shown in Figure 2.

Figure 2: Creating the Thermal/Flow fem

Then create a 3D mesh for the air volume, as shown in Figure 3.

Figure 3: Mesh the air volume only. The structure is not meshed.

3.     Create the Flow Solution

We now create the “Simulation” file, and define a “Flow” analysis. As shown in Figure 4, define a non-turbulent transient analysis. Furthermore, in the “Result Options”, see Figure 5, check the “Pressure and Shear Resultants” box – these will be used for the mapping step.

Figure 4: Flow Solution setup

Then, edit the “Transient Setup” tab as illustrated in Figure 5. 

Figure 5: Results Options for flow forces

Figure 6: Transient setup options

4.     Apply the boundary conditions.

Three boundary conditions are applied:

An inlet of 30 mm/sec at ambient conditions on the –Y faces.

An opening at ambient conditions on the +Y faces.

Slip walls to represent an extended fluid domain on the +X, -X and +Z faces.

As nothing is prescribed on the bottom surface, the solver automatically assumes no-slip, which represents a solid surface. Boundary conditions are shown in Figure 7.

Figure 7: Boundary conditions

We now solve this Flow solution. An example of the flow velocity profiles is shown in Figure 8.

Figure 8: Flow velocity profile.

Mapping the flow forces

1.     Create the structural mesh

Starting with the same part created in step 1, create a new fem file. In the “Edit FEM” window, make sure to choose the NX Nastran (Structural) “Solver Environment”, as shown in Figure 9.

Figure 9: Creating the Structure fem

This time, we will only mesh the structure component and ignore the air volume. See Figure 10. An aluminum material is assigned to the tube.

Figure 10: Structure mesh only. The air volume is not meshed.

2.     Create the Mapping Solution

To map the flow forces to the structural analysis, create a new “Simulation” file and choose a “Thermal-Flow” Solution with a “Mapping” type, as shown in Figure 11. If you leave the “Transient Times” table empty, the solver automatically selects all transient time steps from the flow solution.

Figure 11: Create a Mapping Solution

Next, in the “Optional Output” tab, check the boxes shown in Figure 12 to create the mapping and target Nastran structural solution. A static solution is created. This type of analysis is valid when inertial effects are negligible and where the dynamic content of the flow pressures is well separated from the structures principal modes.

Figure 12: Creating the Mapping and Nastran Solution

3.     Solve the Mapping Solution

Before solving the Mapping Solution, we define a “Mapping Target Set”. This defines the surfaces on which the flow forces will be mapped. Select the cylindrical face of the tube and its free face, as shown in Figure 13 and Figure 14. We can now solve the Mapping Solution. An example of the mapped forces at a given time step is shown in Figure 15.

Figure 13: Mapping Target Set

Figure 14: Select the mapped surfaces

Figure 15: Example of mapped forces

4.     Solve the structural solution

The “Simulation Navigator” now shows one subcase corresponding to each transient time step of the flow solution. See Figure 16.

Figure 16: Subcase created for each transient time step of the flow solution

Before solving, we fix the translational degrees of freedom on the –X face of the tube. Solve the solution.

5.     View displacement results

Next, select a subcase and display the displacement results, as shown in Figure 17. The deformed structure is shown together with the undeformed mesh in Figure 18.

Figure 17: Nodal displacement results

Quick Overview

Although it is well known that Simcenter supports linear buckling solutions (SOL 105), some engineers are reluctant to use this method for composite laminate, based on the perception that the linear buckling analysis does not adequately account for the low transverse shear stiffness of the laminate and is thus not-conservative. This paper demonstrates that Simcenter linear buckling analyses are, in fact, adequate for composite laminates, even for sandwich structures.

Background

Buckling of plates inherently involves large transverse deflections and out-of-plane bending, for which transverse shear becomes significant. Since composite materials have relatively low transverse shear stiffness compared to their in-plane properties, standard plate buckling equations will overestimate the buckling strength of composite laminates.  This error will be larger for thicker laminates.  This behavior is well known to composite structural analysts and nothing new has been presented thus far.

There is this persistent belief among some engineers that the linear buckling solution implemented in engineering simulation software suffers from the same deficiency.  They will instead prefer to use a non-linear finite-element solution to determine the buckling strength of a laminate.  The idea is that the gradually applied load during the non-linear solution will cause it to stop converging when the buckling strength has been exceeded.

This non-linear approach is sound, but does have some caveats:

The onset of instability must be artificially introduced for flat surfaces;

The model could stop converging for reasons other than buckling of the structure, requiring additional interpretation;

The non-linear solution takes more time to solve (Many load steps are needed for an accurate prediction);

The question is therefore whether or not the non-linear approach is worth this extra effort (i.e. Are the results from the linear buckling approach actually not conservative?).

Problem Definition

We will now investigate a buckling problem with the two approaches previously discussed using Simcenter.  Let us begin with a simple 18in by 10in flat plate simply supported on three edges as shown below:

In this first example, we will define an 8-ply laminate [45/0/-45/90]S of T300/5208 (Properties used shown below).

We set-up the boundary conditions as:

At this point, we can readily perform a linear buckling analysis (SOL 105), where we predict a first buckling mode at 181.3lbf (200lbf applied * 0.906538).

We will now verify whether or not we get similar results with a non-linear analysis.  First, because we have a perfectly flat plate, we must artificially introduce the onset of instability by slightly moving a node out of the plane of the plate.  We thus translate a node near the center of the plate as shown below:

If this step was not done, the plate would most likely simply compress but would not bend out of its initial plane.

We now set-up the non-linear solution (SOL 106), selecting the global iterative solver.

Then we set a large number of increments (100 here) and change the convergence criteria as Displacement and Work.

Finally, we change the parameters to account for large displacements:

In order to achieve buckling, the applied load must exceed the critical load. If the applied load is insufficient, we will not know how close to buckling we are.  We set the applied load to 250lbf, well above the critical load predicted by the linear buckling solution.

The last increment of the solution to converge is the 72nd. As a result, we calculate the critical load as 250lbf*72/100=180lbf.  The next increment would have corresponded to a load of 182.5lbf.  We can see that the critical load predicted by the linear buckling analysis fits right between these two values.  At first glance, it seems that linear buckling solution is no less conservative than the non-linear solution.

Let us change the lay-up to [(-45/90/45/0)S_2]S, increasing its thickness to 32 plies as to generate a fair amount of transverse shear stresses.  The linear buckling solution now predicts a critical load of 10,746.6lbf.  Applying 11,000lbf to the non-linear model, we obtain convergence up to increment 97, corresponding to a load of 10,670lbf. This is again just below the SOL 105 prediction.

If we further add a honeycomb core (5056, 3/16” cells, 3.1PCF, 1/8” thick) to the center of this laminate, we increase the buckling critical load to 30,202.8 (according to the SOL 105).  Applying 31,000lbf to the non-linear model, we obtain convergence up to increment 97, corresponding to a load of 30,070lbf.

Conclusion

With these 3 tests, we have shown that the only conservatism coming from using a non-linear solution is due to the incremental nature of the load application.  Indeed the last load for which convergence is observed was found to be below the critical buckling load.  Note that this may not always be the case, depending on the load applied and the number of increments selected to run the non-linear model. Nevertheless, this exercise has shown a clear relation between the results of a linear buckling analysis (SOL 105) and a non-linear analysis (SOL 106), both performed with Simcenter.

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