By Hicham Farid, PhD CAE/FEA Engineer at Aventec

# Introduction

Large architectural, commercial, and residential structures are generally subject to many environmental loads, such as wind, gravity, earthquakes, etc. Understanding how a structure will behave under these loads is crucial not only for its structural integrity, but also for the safety of the public. Civil engineers usually perform a structural analysis in order to ensure the reliability and safety of buildings. These analysis/calculations are often subject to approximations and high safety factors, leading to over-designed structures that are not necessarily safe. To top it off, this over-engineering also contributes to cost overages, over-spend, and introduce more friction into the construction lifecycle.

When performing a deep level of structural analysis using sophisticated tools such as FEA, engineers stumble into the challenge of large models. Often these models present a high level of understanding of how a structure will behave due to an applied load. While we might need some result in some local areas, refining the mesh could make the matter far worse in term of model size.

In this paper, I will be presenting a solution to overcome this issue using submodeling. First, a full scale global model of a steel structure subjected to gravity and a dynamic seismic load will be prepared. This model will be used to generate boundary conditions to drive the subsequent submodel analysis for a more refined local analysis under the same loading conditions. A third analysis is performed by adding more geometrical details to the submodel for more investigative analysis.

# Global Model Setup: Gravity and Seismic load

The global model I have considered in this paper is a simple multi-story steel building subjected to gravity and a dynamic seismic load. The seismic load I considered was based on the Vrancea Earthquake field data. I applied these data as acceleration time’s amplitude using dynamic implicit procedure.

I reduced the provided data by a factor of ten in order to make the model run faster for a quick turnaround. The new time scale is therefore ten times shorter than the actual recorded field data.

As shown in Figure 1, the multistory building consists of six floors having the same structural pattern. I meshed the model at the part level using 4689 C3D4 elements. I used a default coarse mesh size of 0.64m for a faster analysis turnaround.

The boundary conditions applied were to restrain the displacements in the X and Y directions at the building’s base. An acceleration of a unit magnitude was applied, amplitude data were used to enforce the earthquake scenario. Wind load was not considered in this work. Results are reported in Figure 5. Stresses are concentrated locally at the first floor’s support beams.

# Submodel

Global model is running and yielding proper results as expected. Let’s dive into how to prepare the submodel and get more accurate results locally. As mentioned above, the global model will be used to drive the submodel, or the submodel’s boundary conditions will be based/extracted from the global model. I am more interested to see how stresses are distributed locally at the support beam level of the first (main) floor, therefore the submodel will be a cut around that area with some local mesh refinement.

First, I copied the global model. Once the global model is copied, we have to specify that the new model is actually a submodel. From the Edit Attribute menu, under submodel tab, toggle on Read data form job, then specify the global model .odb file. Note that the Submodel and the global model have to be located under the same directory.

Then used the geometry edit tools to eliminate the undesired geometry sections. The final profile is illustrated in Figure 8 and Figure 9.

Here, I meshed the Submodel with 16,335 C3D10 tetrahedral elements.

There are two different ways or techniques to perform a submodeling simulation; Node-based submodeling and Surface-based submodeling. In the first technique, the nodal results field is interpolated onto the Submodel nodes, while in the second, stress field is interpolated onto Submodel surface integration points. The node-based submodeling is more general and more common. The surface-based technique is limited to general static procedure and offers only solid-to-solid submodeling. The dynamic nature of the earthquake model dictates the use of node-based submodeling technique for this specific example.

In the Submodel we have here, gravity load is applied as per the global model, then local boundary conditions are applied at the cut facets as shown in Figure 10.

When using node-based submodeling, the global model is used to drive the Submodel using a boundary condition, while when using surface-based submodeling, the driver model is implemented as a load.

In the create Boundary Condition menu, click Other and then Submodel. Edit Boundary Condition window will pop-up. Define the Submodel set by picking up the cut facets. Here, I predefined a set at the part level which makes the boundary condition definition fast and easy. No other boundary condition definition is needed.

As results verification and validation for the Submodel, I will be plotting displacements, velocities, and accelerations at the same location from both the global and the Submodel. The picked node for the results plots is shown in Figure 14.

Displacements and velocities in both the global model and the Submodel are showing very good correlations. However, we observe peaks in accelerations in the Submodel that are orders of magnitude higher than the global model and the filed data, this is highly due to the dynamic nature of the analysis.

# Submodel: Adding Geometrical Features

In submodeling, geometrical feature can be added to provide a deeper insight to the results. Holes, cuts, grooves, bolts, etc. can be considered. To illustrate this, I added beam profiles to the support and the cross beams in the submodel; the cross beam has an L profile while the support beams have a U profile as illustrated in Figure 18.

The modified submodel is prepared similarly to the previous submodel; the global was copied and the node-based submodeling technique was used. The same topology and size was used. Stress and displacement results are reported in Figure 19 and Figure 20. We can see that the stress contours and magnitude is the same. A higher stress concentration at the top cross beam.

# Summary

· A seismic analysis was performed on a multi-story steel structure.

· Earthquake ground motion records acceleration from Vrancea Earthquake were used to drive the dynamic global.

· A submodel was used to analyze local results using node-based submodeling technique.

· A modified submodel was also presented to show the possibility to add geometrical feature to a submodel.

# Conclusion

When dealing with big models, the challenge is always to reach a compromise between model fidelity and size. We need constantly to keep refining the mesh in order to get more realistic results, which makes a simple model orders of magnitudes heavier on memory.

In this paper, we showed how using submodeling technique can be very useful and efficient when dealing with big models because it substitutes the whole model mesh refinement process with a more local sub model that is driven by results previously obtained by larger global models.

# References

V. Inculet, Nonlinear analysis of earthquake-induced vibrations, Masters’ Thesis, Aalborg University, 2016.

# Acknowledgement

I would like to thank Vlad Inculet for sharing his field data from the Vrancea Earthquake of 1977 in Romania. Vlad was nice enough to provide a full excel spreadsheet that contains data of acceleration versus time as recorded in the field.