# Mastering Mesh Size in Finite Element Models: Importance, Effects, and Best Practices

Introduction:

Finite element analysis (FEA) is a widely used numerical simulation method for solving complex engineering problems. FEA works by dividing the geometry of the structure into a finite number of elements, each of which is analyzed separately. One of the most critical factors affecting the accuracy and reliability of FEA results is the mesh size. In this article, we will discuss the importance of mesh size in finite element models and how it affects the accuracy of FEA simulations.

The Importance of Mesh Size in Finite Element Models:

Mesh size is an essential parameter in the FEA process as it influences the accuracy of the results obtained. In FEA, the geometry of the structure is divided into small elements, and the equations governing the behavior of these elements are solved iteratively to determine the response of the system to different loads. The mesh size determines the level of detail captured in the analysis, and therefore, it is critical to choose the appropriate mesh size for a given problem.

If the mesh size is too large, it can lead to inaccurate results. This is because the larger elements do not capture the small-scale features of the structure, leading to a loss of information. As a result, the calculated stresses and strains may be underestimated, and the model may fail to capture the local behavior of the structure. For example, if a crack is present in the structure, a coarse mesh may not capture the stress concentration around the crack tip, leading to inaccurate results.

On the other hand, if the mesh size is too small, it can lead to overly complex and computationally expensive models. This is because more elements are required to discretize the structure, increasing the computational time required to solve the equations. In addition, small elements can cause numerical instabilities in the analysis, leading to non-physical results. For example, when the mesh size is too small, the elements can become distorted, leading to mesh-dependent solutions, which are not unique and may produce spurious results.

The Effect of Mesh Size on FEA Results:

The choice of mesh size has a significant impact on the accuracy of FEA results. In general, the smaller the mesh size, the more accurate the results. However, as mentioned earlier, the computational cost of a simulation increases with smaller mesh sizes. The choice of mesh size should be based on the level of accuracy required and the available computational resources.

When the mesh size is too large, the analysis may underestimate the stress and strain concentrations, leading to inaccurate results. Consider this example for better understanding. By extracting the stresses resulting from the analysis of 5 models of a bracket with different mesh sizes (figure 1), it is easy to draw the mesh density curve against the maximum Mises stress for a point of the bracket.
As shown in the second figure, the increase in stresses after analyzing the bracket with 1000 elements has led to a lower slope, so that if 7000 elements are considered for the member; compared to 23,000 elements; 6.5% of the tension difference is reported.

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