Understanding Elements In Finite Element Analysis

 

Simulations have drastically reduced the time taken to design and manufacture new components. With the help of simulations the failure locations can be identified without performing the physical test in the prototype. This reduces the time taken to analyze the component and cost of the analysis. The advent of modern FEA techniques has transformed the engineering industry. 

 

Finite element Analysis (FEA) breaks down a large component into discrete smaller elements and then applies the governing differential equations, also known as Partial Differential Equations (PDEs) on the nodes where it computes simulation variables. FEA enables companies to save money and time by simulating the real time physics on the 3D models. 

 

Why Do We Need Meshing in FEA?

Finite element Analysis software dicritises a component and breaks it into constituent elements. The software then applies governing differential equations to each nodes. By applying the numerical methods the GDE is converted to matrices which are solved to get the nodal values (stress, temperature and deformation). With the help of the nodal values, the engineer can ascertain areas where the geometry will buckle under the application of external stress. 

This process of the creation of cells or elements is called meshing.

 

The resolution of a mesh often creates variable mesh models, affecting the solution's quality. Mesh flow smoothens out this geometry cluster and creates uniform mesh elements. A simple thought experiment to visualize mesh flow would be to take a crumpled sheet of paper and iron out the wrinkles on the paper. 

 

Different geometries need different approaches to generate a mesh. It is easier to create a 1D mesh than to create 2D and 3D meshes. The first step in creating a 1D mesh involves the preparation of a cross-section of the component along the centroidal axis of its geometry. 2D mesh consider mid surfaces when the thickness of the geometry is less than 5 mm, in this scenario the load effect over the thickness will be very low 

 

Effects of Mesh Density on Finite Element Analysis

Mesh density is the number of mesh elements in any given geometric location. An increase in the mesh density will lead to increased utilization of processing power and RAM. This is why most FEA software uses a combination of both 3D and 2D elements to improve the accuracy of the solution while reducing the processing time while running the simulation. 

 

Engineers should also consider the properties of mesh to get a better convergence while solving the simulations. A FEA tool discretizes a 3D CAD model, based on the parameter specified by the engineer. The initial mesh density is based on various factors, including high-stress areas or boundaries between two parts or components. 

 

The size of mesh elements should adhere to conditions that will reduce the processing time while increasing the accuracy of the result. Tet and Hex elements are the most commonly used mesh elements.

 

Different Types of Mesh Elements

Mesh size and quality are the factors that all engineers should consider while meshing. The three prominent elements variants are, 1D, 2D, 3D, and special mesh elements. Each of these mesh elements solves for a different geometric property: length, area, and volume. The mesh elements are divided into different sizes and shapes based on their geometry. The coarse elements require less memory to discretize, while the smaller elements increase the accuracy of the FEA result. 

 

Engineers spend a great deal of time choosing the correct size of the mesh and ensuring the required refinement of the mesh because any deviation can result in unrealistic results. 

 

Three primary mesh elements are divided along the basis of their Degrees Of Freedom (DOF). The DOF is the rotational and transformational movement of the element along its axis. 

 

The different types of mesh elements are as follows. 

 

1D - Line element 

 

2D - Tria (triangle) and Quadrilateral 

 

3D - Tet (Tetrahedron), Prism, polyhedron and Pyramid

 

1D Element

Creating codes for automation is easier when dealing with 1D elements. The simplest elementis the 1D element used to create a mesh for structures like a beam, column, bar and shafts. The 1D element only has two nodes reducing the time taken to solve the elements between these two points. 

 

2D Elements 

The primary elements in a 2D mesh are tria (triangle) and quad (quadrilateral/square). These elements discretize geometries faster than 3D elements  while requiring more memory. The engineer has to create assumptions about the external forces acting on the component.  Simulation models with 2D elements allows engineer to consider only the forces which are in transverse direction to the 2D plane. Since the thickness of the 2D element is 0, it is given as an additional input to the solver

 

3D Elements

 

The primary element in a 3D mesh is a Tet (tetrahedron), Hex, Prism, and a Pyramid. Creating a 3D mesh structure is much more difficult than generating a 1D or 2D mesh. 3D mesh requires higher memory capacity for discretizing. This difficulty increases the computational time taken to resolve a 3D mesh. The complexity of the 3D mesh will overwhelm the engineer in finding errors in the mesh. Most engineering firms recommend generating a 3D element as the final step in their FEA process. Almost all components can be de-featured from a 3D CAD drawing and converted into a simpler 3D mesh. This combination of 2D and 3D meshes will improve the accuracy of the FEA result and help the engineers to create a stable component. 

 

Three different types of elements are used to create a mesh. They are differentiated based on their degrees of freedom. The dimensions determine the processing power needed to resolve the mesh. All engineering firms use a mix of all three elements to generate a mesh that reduces the processing time while maintaining high accuracy of the result 

 

Factors That Decide the Type of the Mesh

 

• The size and shape of the model 
• The type of analysis 
• The quality of results expected 

 

Every engineering component exits as a 3D object, but to reduce the computational power and complexity of the geometry engineers convert the CAD drawing into its 1D and 2D meshed models. 

An analysis type is one of the primary factors determining the type of mesh.Tet andd Tri elements are predominantly used in most of the FEA simulations and the Hex elements are used in specific simulations where planar stresses are dominant.  

The final factor determining the type of element used in a mesh is the time taken to complete the analysis. Every major FEA tools recomends automatic meshing as automatic meshing incorporates meshing methods and parameters to get a optimal refinement in critical locations and optimal simulation time.

 

Conclusion

Creating a mesh is a fundamental part of FEA. FEA have played a vital role in reducing the time taken to manufacture new components while increasing their structural integrity. 

 

Project management is a skill set that all engineers, especially design and CFD,  should develop throughout their careers. FEA Engineers must define their mesh elements based on the accuracy and time allotted for each project. In an ideal world, engineers can use 3D meshing on all their components and take days, if not months, to solve their mesh.

 

One of the easiest ways to learn about time management and mesh selection is to enrol in Skill-Lync's PG Program in FEA engineering. We use real-world projects to train our students in FEA fundamentals, helping them select the correct mesh elements. Upon completion, our students can start their careers as CAE Engineers, CAE Analysts, CAE Automation engineers, and CAE Durability engineers.

 

Take the first step towards your future career by enrolling in our designed FEA engineering program.