How to ensure the Mesh is good enough for accurate simulation? | Mesh Convergence in Abaqus

Summary

This tutorial explains mesh convergence in finite element analysis (FEA), with a focus on how mesh density affects simulation results. It covers different methods to achieve mesh convergence, such as the H and P methods, using a case study on a connecting lug. The tutorial highlights the importance of mesh refinement in accurate displacement and stress predictions, discussing the limitations posed by singularities and localization problems. Practical tips are provided on controlling singularities, refining meshes for large models, and focusing refinement in areas of high stress. The video also touches on submodeling techniques to achieve detailed results.

Takeaways

• 😀 Mesh convergence in FEA ensures that the solution stabilizes as the mesh density increases.
• 😀 Convergence refers to the solution approaching a specific value, similar to how light converges through a lens.
• 😀 The two primary methods for achieving mesh convergence are the H-method (increasing elements) and P-method (increasing polynomial order).
• 😀 Mesh convergence can be studied by comparing results at different mesh densities, such as coarse, normal, fine, and very fine.
• 😀 Displacement predictions tend to converge quickly with mesh refinement, while stress predictions require much finer meshes, especially in areas with high stress concentration.
• 😀 Stress singularities can occur at sharp corners or point loads, where stress values theoretically tend toward infinity with mesh refinement.
• 😀 Localization problems arise when mesh refinement in certain regions leads to unrealistic stress responses, such as the post-peak behavior in a material.
• 😀 Singularities, like those at sharp corners, typically don't converge to a meaningful value, and can be ignored in overall model analysis if they don't significantly impact the structure's response.
• 😀 When working with complex models, computational resources may limit mesh refinement, and submodeling can help focus on specific areas of interest with finer meshes.
• 😀 It’s rarely necessary to use a uniformly fine mesh across the entire model; instead, focus on refining the mesh in high-stress areas to balance accuracy and efficiency.
• 😀 Abaqus can be used to identify regions of high stress and perform mesh refinement only in those regions, saving computational resources while ensuring accurate results.

Q & A

What is convergence in the context of finite element analysis (FEA)?

Convergence in FEA refers to the behavior of a numerical solution as the mesh density increases, eventually leading to a solution that approaches a unique value. This is similar to the mathematical concept of convergence of a sequence, where terms gradually approach a specific limit.

What are the two primary methods for achieving mesh convergence in FEA?

The two main methods for achieving mesh convergence are the H-method, which refines the mesh by increasing the number of elements while keeping the polynomial order constant, and the P-method, which increases the polynomial order of the interpolation function while keeping the number of elements constant.

What is the role of mesh size in ensuring the accuracy of FEA simulations?

Mesh size plays a crucial role in the accuracy of FEA simulations. A sufficiently refined mesh ensures that the results are reliable. As the mesh is refined, the numerical solution tends to converge towards a unique value, but beyond a certain point, further mesh refinement produces negligible changes.

How do we identify if the mesh has converged during an FEA simulation?

Mesh convergence is identified when further refinement of the mesh results in negligible changes in the solution. In a convergence plot, this is reflected by a plateau, where the solution no longer significantly changes as the mesh density increases.

What are the mesh densities used in the case study of the connecting lug model?

The case study of the connecting lug model uses four different mesh densities: coarse (14 elements), normal (112 elements), fine (448 elements), and very fine (1792 elements).

Why is it important to use a fine mesh for stress calculations near stress concentrations?

A fine mesh is necessary near stress concentrations because stress and strain are calculated from displacement gradients. A finer mesh is required to accurately capture these gradients, particularly in regions of high stress or sharp geometrical features.

What challenges are associated with predicting stress at singularity points in FEA models?

At singularity points, such as sharp re-entrant corners or points of contact, the stress theoretically becomes infinite. No matter how much the mesh is refined, the stress will continue to increase, leading to an inaccurate result. These singularities are a result of the idealizations in the FEA model, like sharp corners or rigid connections.

What are stress singularities, and how do they impact FEA results?

Stress singularities occur at points where stress does not converge to a specific value as the mesh is refined. These typically occur in situations with point loads, sharp corners, or points of contact. While they lead to inaccurate stress predictions at those points, they usually have negligible effect on the overall behavior of the model.

What is the concept of localization in FEA, and how does it affect mesh convergence?

Localization in FEA refers to the phenomenon where deformation becomes concentrated in one element due to high local stress levels. As a result, the global response of the model, including load-deflection behavior, can be heavily influenced by the mesh density in the localized area, making convergence difficult in post-peak regions.

How can one handle singularities and localization when conducting mesh convergence studies in FEA?

To handle singularities, it's common to omit small details, like fillets, to simplify the model, though this may lead to inaccuracies in stress predictions near the singularity. For localization problems, it's important to consider the mesh density in areas where high deformation occurs and to interpret the global response cautiously, especially in post-peak regions.