Everything That You Need To Know About Meshing in FEA

Any machine in the world is the assembly of several components. Aggregation of each of those components with some constraints leads to the desired output. Take the example of a car. The car has several assemblies - chassis assembly, door assembly, etc. Each of those assemblies has several components, take for example the door assembly, from the door hinge to the sheet metal and plastics there are numerous components. The shapes of the components are complex and the environment in which the components act could be challenging. Hence, engineers should evaluate the impact of various forces acting on a system, and calculate the ability of the system to function as desired in the given conditions. Let us look at an example to better understand how engineers can monitor and evaluate the forces acting on a system. 

Consider a simple cuboid fixed to one end as a cantilever. And consider a uniform axial force that pulls the cuboid. We can calculate the impact of this force on the system using simple calculations.

 

 

Now, let us consider a hook as the component. You would understand that the shape is complex, and the calculation is complex. Hence to simplify the simulation, it is broken down into smaller elements and we study the impact of various forces on each of those small elements. This exercise of breaking a larger component into many small elements is called meshing. It is then extrapolated to the whole system to arrive at an accurate solution.

 

 

The analysis of these smaller elements after the application of Partial Differential Equations (PDEs) is called Finite Element Analysis (FEA)

What Is Mesh Convergence in FEA?

The size and resolution of the mesh directly affect the results of FEA. Sometimes reducing the size of the mesh and increasing the mesh elements can drastically change the results. Mesh convergence is the process of analysing the size of the mesh and determining the correct mesh element for an optimized result. Mesh convergence is done by reducing the size of elements in an iterative manner and checking the accuracy of results. 

Types of Mesh Elements in FEA

Broadly speaking there are three types of mesh elements in FEA; 1D, 2D, and 3D. 

• A 1D mesh element is applied to slender bodies or beams and it contains only two nodes. 
• 2D meshing is done for shells and sheet metals for which the thickness is less. A 2D mesh has three or four nodes and computing is easier when compared to 3D meshing.
• 3D meshing is the most often used technique in FEA. A 3D mesh element has more than 3 nodes on each of its faces.

The complexity of analyzing the component increases from 2D to 3D. The selection of the type of mesh is a function of the accuracy required and the time available to process the component. In 2D meshing, tri (triangles) and quads (quadrilaterals) are the most frequently used cell shape. In 3D, we have a lot of types. It could be a tetrahedron, pyramid, triangular prism, hexahedron, polyhedron, etc.

Differences Between Solid Meshing and Shell Meshing

A shell is a body that has an outer surface and is hollow inside. Whereas a solid body has material throughout the entire geometry of the body. We have different meshing techniques for solid and shell. 

• Shell meshing is suitable for thin components, while solid meshing is not limited to thin components.
• Shell meshing has 6 Degrees Of Freedom (rotational and translational along x,y, and z axes), while solid meshing has 3 degrees of freedom. Degrees Of Freedom can be defined as the rotational and transformational movement of an element along its nodes. 
• Shell meshing uses 2D elements whereas solid meshing involves 3D elements. 

Engineers follow a  rule of thumb when selecting from either solid or shell meshing. A quick guide to determining shell or solid meshing is to identify the ratio of thickness to the length of the component. If the thickness to length is larger then the shear stress has a huge impact. Therefore solid meshing has to be done. If the thickness to length ratio is small then the shear stress and negligible and we can perform shell meshing.

Factors That Influence Mesh Quality

• Aspect ratio
• Skewness
• Jacobian

Aspect ratio

The aspect ratio is the ratio of the largest length of the element to the smallest length of the element. It is recommended that this ratio is maintained at a number lower than 5.

Skewness

The degree to which an element’s angular measure is different from the ideal element type is called skewness. Skewness should be less than 45 degrees.

Jacobian

Jacobian is the measure of distortion of an element’s shape to the ideal element’s shape. Jacobian, should be greater than 0.6. For most components, the elements close to the curvature would have a higher aspect ratio and Jacobian. The focus should be to refine the mosh locally to improve the mesh quality.

These are some of the typical quality checks to ensure good mesh quality.

Conclusion

Choosing the right element and shape for meshing is essential to the successful design of a component, making the most important step in FEA. Pursuing a PG program in FEA will help you understand these concepts better. Our student Nirmal Kumar has successfully created a solid mesh for a rearview mirror. Working on this project helped him to to lear how to create mesh using tria and ortho tria elements, clearing errors and applying volume mesh.