Finite Element Analysis (FEA, Finite Element Analysis) is a widely used numerical computation method in the fields of engineering design and structural mechanics, which is used to solve complex partial differential equations. In the process of finite element analysis, mesh generation is a crucial step. It not only affects the accuracy of the calculation results but also directly relates to the efficiency of the solution and the consumption of computing resources. Therefore, how to reasonably carry out mesh generation is a problem that must be seriously treated when performing finite element simulation.



1. Basic Concepts of Mesh Generation



Mesh generation is the process of discretizing a continuous geometric model into a finite number of elements. These elements are connected by nodes to form a mathematical model that can approximate the original structure. Common element types include triangular elements, quadrilateral elements, tetrahedral elements, and hexahedral elements, among others. According to the geometric complexity and precision requirements of the analysis object, appropriate element types can be selected for meshing.



Chapter 2: Principles of Mesh Generation



In the process of mesh generation, the following basic principles should be followed:



1. Meet the accuracy requirements: in areas of stress concentration or severe geometric changes, the mesh should be appropriately densified; while in regions with uniform structures and gentle changes, coarser meshes can be used to save computational resources.

2. Ensure element quality: avoid deformed elements (such as excessively flat or long elements), otherwise it will affect the stability and accuracy of the calculation results.

3. Consider boundary conditions and load distribution: ensure that the mesh can accurately reflect the actual boundary conditions and external force loading methods.

4. Take into account the computational efficiency: an overly dense mesh will cause a dramatic increase in computational volume and extend the solution time, so it is necessary to weigh accuracy and efficiency.



Chapter 3: Common Mesh Generation Methods



1. Free Meshing

Suitable for models with complex shapes. The system automatically selects an appropriate element type (such as triangles or tetrahedra) for filling. The advantage is high degree of automation, but the disadvantage is that the quality of the elements is difficult to control, and the accuracy is relatively low.



2. Mapped Meshing

Generally used for regular geometric shapes, such as rectangles and cylinders. By specifying the direction to divide the mesh, quadrilateral or hexahedral elements are generated, which have higher computational accuracy and convergence.



3. Sweep Meshing

Suitable for three-dimensional models with stretching or rotation characteristics. By 'sweeping' the two-dimensional mesh along a certain direction to generate a three-dimensional mesh, it has high controllability and accuracy.



4. Adaptive Meshing

In the process of solving, local mesh density is automatically adjusted according to the error estimation to improve the accuracy of the results. This method is widely used in engineering analysis with high precision requirements.



Chapter 4: Quality Assessment of Mesh Generation



After the mesh generation is completed, quality assessment is also required. Common quality indicators include:



- Aspect ratio: measures the degree of stretching of the element;

- Skewness: evaluates the non-orthogonal degree of the element;

- Jacobian determinant: determines whether the element has deformed;

- Uniformity of node distribution: affects numerical stability.



Conclusion



In summary, mesh generation as a key step in finite element analysis directly affects the reliability and efficiency of the calculation results. A reasonable mesh generation strategy not only needs to consider the changes in geometric features and physical fields, but also needs to be optimized in combination with the actual engineering requirements. With the development of computer technology and finite element software, adaptive mesh technology and intelligent partitioning algorithms are gradually maturing, providing strong support for improving analysis accuracy. Therefore, in practical engineering applications, mastering scientific mesh generation methods is of great significance for improving analysis efficiency and result accuracy.