What Is Convergence Testing In FEA?

Finite Element Analysis (FEA) is a powerful tool widely used in engineering to evaluate the structural integrity, heat transfer capabilities, fluid dynamics, and other physical aspects of designs. 

A pivotal aspect of FEA is convergence testing – a process that ensures the accuracy of the results by optimizing the mesh size in the model. 

Convergence testing in FEA involves refining the mesh to ensure that the solution becomes more accurate as the mesh is refined. It verifies that the results converge towards a stable solution by evaluating changes in the solution with each refinement. It helps determine an optimal mesh size for reliable and accurate analysis.

Although seemingly complex, understanding convergence testing is crucial for any FEA user. 

In this article, I will explain the concept of mesh convergence testing, why it is needed, how to conduct a convergence test, and whether it is necessary to check for convergence on every model.

mesh convergence

What Is Convergence Testing In FEA?

Convergence testing in Finite Element Analysis (FEA) is a crucial process that involves examining the accuracy of a simulation by adjusting and refining the mesh size. 

In essence, it is a sequence of evaluations where the mesh, which is the collection of small elements representing the model’s geometry, is systematically refined to achieve a stable and precise solution. 

The concept underlying convergence testing is that the solution should approach a fixed, “true” value as the mesh is made finer. 

If the solution varies significantly with changes in the mesh, the results may not be reliable. Therefore, conducting a convergence test is a critical step in ensuring the reliability of FEA results.

Why Is Mesh Convergence Needed?

For several reasons, mesh convergence is indispensable to Finite Element Analysis (FEA). The primary purpose is to ensure the reliability of the solution. 

In FEA, the solution’s accuracy is directly tied to the mesh’s density. A coarser mesh may lead to less accurate results, while an overly fine mesh can result in unnecessary computational expense and time. 

Mesh convergence balances these extremes, refining the mesh until the solution changes negligibly with further refinement. This guarantees that the FEA results are not significantly influenced by the mesh size but rather represent a true solution within a specified tolerance. 

Moreover, mesh convergence checks help to avoid the pitfall of solution divergence, where variations in the solution become unbounded with increasing mesh density. 

Thus, mesh convergence is an essential step in verifying the integrity and reliability of FEA calculations.

How Do You Conduct A Convergence Test?

Conducting a convergence test in Finite Element Analysis (FEA) follows a systematic process. 

The first step involves initiating the analysis with a coarse mesh. After obtaining the results, refine the mesh incrementally, each time noting the changes in the solution. 

This process is repeated until a point where further refinement in the mesh does not significantly alter the output – this is referred to as the point of convergence. 

Plotting the output values against the mesh size or the number of elements can visually represent this. The graph should ideally show the solution stabilizing as the mesh is refined. If the solution continues to oscillate or diverge, it indicates issues with the model setup or the quality of the mesh, requiring further investigation. 

Remember, the goal is to achieve a balance where the solution is adequately accurate without imposing excessive computational demands. 

In essence, the convergence test ensures the reliability of the simulation by confirming that the results are not heavily influenced by the mesh size but are indeed representative of the true solution.

Do I Have To Check For Convergence Every Time?

Checking for convergence in every Finite Element Analysis (FEA) is generally highly recommended, especially for complex or critical simulations. However, this may not always be necessary or practical in all scenarios due to time and computational limitations. 

If the FEA model is similar to a previous analysis that has already been validated with a convergence test, and you are confident in the mesh quality and element types used, then it might be acceptable to bypass a full convergence study. 

For example, I often repeat simulations, which are variations of similar products. Knowing the products well and having experience, I am very confident in my mesh size as I have had similar simulations verified with similar mesh sizes in the past. As most of the simulation work I do is time-sensitive, if I am very confident in my mesh size, I have the experience and knowledge to skip this set. 

However, be aware that this does carry a risk. 

Skipping the convergence check could potentially compromise the reliability of the results. Therefore, it is essential to make an informed decision based on the nature of the analysis, the complexity of the model, and the required level of confidence in the results. 

Remember, the convergence test is a best practice to ensure the accuracy and reliability of your FEA results and should not be overlooked without careful consideration.

How Long Does Convergence Testing Take?

The duration of convergence testing in Finite Element Analysis (FEA) can vary greatly and largely depends on a number of factors, including the complexity of the model, the power of your computational resources, and the level of detail required in your results.

A simple model with a small size and less complexity may take only a few hours to complete a convergence test. However, for more complex models, especially those featuring non-linear materials, large deformations, or intricate interactions, convergence testing could take several days or even weeks. 

It’s important to take these factors into account when planning your analysis. While convergence testing does require additional time, the assurance of reliable and accurate results is often well worth the time investment.

How Do I Know If My Convergence Testing Is Accurate?

Assessing the accuracy of your convergence testing in Finite Element Analysis (FEA) involves a few crucial steps. The first indicator is the stabilization of your solution with incremental mesh refinement. If your solution continues to fluctuate significantly with finer meshes, your model might not have reached convergence, or there may be issues with your model setup or mesh quality. 

It’s a good practice to plot the solution against the mesh refinement level or number of elements. An ideal scenario is when the solution becomes stable and does not significantly change with further mesh refinement. This reflects a state of convergence, which indicates the accuracy of your testing.

Also, remember that the true solution will never be known exactly in a real-world problem. Therefore, you can estimate the error of the solution by comparing the solutions obtained from two successive mesh refinements. This process, known as error estimation, offers an additional check to ensure that your convergence testing is accurate and the results are reliable.

Keep in mind that convergence testing is not just a one-time process and should be performed every time significant changes are made to the model geometry, boundary conditions, or loading scenarios. This ensures the fidelity and accuracy of your FEA results.

Can Convergence Testing In FEA Detect Errors In Model Setup?

Convergence testing in Finite Element Analysis (FEA) can often detect errors in the model setup. 

When the results of your analysis continue to oscillate or diverge even with mesh refinement, it can be an indicator of problems with the model or the quality of the mesh. This could include issues such as inappropriate boundary conditions, incorrect material properties, or inaccurate loading scenarios. Therefore, convergence testing can serve as a useful check for the integrity and accuracy of your model setup. 

However, it’s important to note that while convergence testing can help identify potential errors, it shouldn’t be relied upon as the sole method of model verification. It should be used in conjunction with other verification techniques and physical testing to ensure the overall validity and reliability of your FEA results.

Final Thoughts

Convergence testing is a critical aspect of Finite Element Analysis (FEA) that ensures the reliability and accuracy of simulation results. While it may be tempting to bypass this step due to time constraints or familiarity with similar models, it’s crucial to remember that each FEA is unique and may present its own set of challenges. 

Convergence testing acts as a checkpoint to detect errors in the model setup and reaffirm that the solution is not significantly influenced by the mesh size. It enables us to strike an effective balance between computation time and solution accuracy. 

Overlooking this process could potentially risk the validity of your FEA results. Therefore, irrespective of the complexity of the model or the urgency of the project, convergence testing remains an essential practice in FEA.

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