Finite Element Analysis (FEA) uses a geometrical mesh made up of nodes and elements to simulate a wide range of physical interactions. This allows for engineers to gain insight and optimize design performance prior to investing in an expensive physical prototypes.

## What are FEA Nodes & Elements?

Elements are made up of at least 2 nodes. Nodes are points at which exact solutions are calculated. Between nodes of a single element solutions are estimated through using interpolation.

## Improving FEA Result Accuracy

#### Reducing Element Size

The most straight forward way to improve accuracy is to make your elements smaller. Where results are not changing significantly between nodal points this is unnecessary. However, points at which significant changes do occur over a short distance such as at corners or holes this is necessary to gain an accurate result.

One issue with simply using smaller elements is that most physical phenomena aren’t estimated well by linear interpolation. Most results are based on the square or cube of a variable meaning the results between nodes won’t change linearly, but instead quadratically.

#### Adding More Nodes Per Element

One of the best ways to increase the accuracy of a simulation is to use more nodes in an element. This opens up the ability to use quadratic or higher order interpolation instead of linear interpolation. Adding a 3rd node in the center of an element is so effective at increasing accuracy that the majority of FEA software including ANSYS start with a 3 node beam (BEAM3) as their simplest element.

## Understanding How FEA Calculates Stress

Most structures of interest today are statically indeterminate meaning they have more internal forces and reactions than there are static equilibrium equations. In other words, statically indeterminate structures have more variables that you need to solve for than they have equations making finding a solution using the standard static method impossible.

There multiple methods to solve statically indeterminate problems.

- Flexibility Method – Hand Calculations and Occasional FEA
- Slope-Deflection Method – Hand Calculation Method
- General Stiffness Method – Method Used By Most FEA Software

#### General Stiffness Method – aka Displacement Method

The General Stiffness Method is a modified form of the Slope-Deflection Method. The General Stiffness Method calculates the displacement at each node and then uses interpolation over the elements to determine the solution. In order to calculate stress you need to first derive strain from the deformation solution and then can use the stress strain curve to convert the strain to stress.

#### Understanding Strain and FEA

Strain = Change in Length / Initial Total Length

Strain is a unitless value which can be directly related to Stress using stress-strain curves from material properties. Stain is a derivative of stress, which means that if you have a linear stress plot, the strain will be constant. Having a linear stress plot and therefore a constant strain and stress over an element can cause significant issues with the accuracy of FEA results as will be seen later.

## Types of FEA Elements

### 1D or Line or Beam Elements

1D Line Elements such as beams have the capability of simulating tension, compression and bending. The number of degrees of freedom (DOF) at each node depends upon the type of analysis being used. In a 2D analysis, each node has 3 DOF (x, y, rotation). In a 3D analysis, each node has 6 DOF (x, y, z, x-rot, y-rot, z-rot).

#### When Not To Use

- When buckling may occur and control.
- When hoop effects are present
- When local stresses may control such as bolt tear out, block shear, etc…
- When torsion is present.
- Any other applications that aren’t in pure tension, compression, or bending.

#### Advantages

- Extremely simple element type which provides rapid solutions when it’s limitations are acceptable.

### 2D or Planar Elements

2D Elements can be used to analyze sheet metal and similar structures. These are many times the most common type of elements being used in FEA. They combine far faster computation time compared to 3D Elements while maintaining accurate results for most cases.

##### Limitations

- Can not calculate out of plane stress or failure mechanics.

#### Triangle 2D Elements

##### TRI3 – Triangle with 3 Nodes

As a general rule of thumb, the fewer elements you have the less accurate your result will be. Just using this logic it would be obvious the the TRI3 is the worst 2D element, however the TRI3 element has additional issues. the TRI3 element has issues with stiffness.

TRI3 allows the FEA solver to generate a linear plane to interpolate deformation from using the 3 provided nodal points. This causes an issue with the accuracy of the FEA solution because, as mentioned previously in “Understanding Strain and FEA”, a linear plane of deformation generates a constant strain and therefore stress over an entire element. In reality stress is always constantly changing as you move along a structure making the constant strain and stress over an element very inaccurate. For this reason TRI3 elements have a tendency to form results with too much stiffness and therefore undervalue stress leading results.

TRI3 Elements do have one advantage, if the analysis is simple enough and you use enough TRI3 elements they can generate results very quickly.

##### TRI6 – Triangle with 6 Nodes

TRI6 is a second-order or quadratic version of TRI3. Being a second-order provides one big advantage, FEA is no longer limited to using a linear plane of deformation. Using a polynomial plot for deformation allows the software to apply a linear plot of stress and strain improving accuracy over TRI3 dramatically. However, TRI6 still have stiffness issues as with any triangle element making them less accurate than other 2D elements.

The downside of the TRI6 compared to the TRI3 is with 2x the nodes it will demand substantially more computational power and time.

#### Quadrilateral 2D Elements

##### QUAD4 – Quadrilateral (rectangle) with 4 Nodes

QUAD4 elements are a step above TRI3 elements as they have reduced stiffness and therefore increased accuracy. However, QUAD4 elements are first-order elements meaning they rely on linear trends between exterior nodal points which substantially reduces the accuracy of interpolated results.

QUAD4 Elements offer fast calculations with more accurate stiffness compared to TRI3 elements.

##### QUAD8 – Quadrilateral (rectangle) with 8 Nodes

QUAD8 Elements are a a second order version of QUAD4 elements delivering the improved accuracy of quadratic equations during interpolation. With the improved interpolation accuracy also comes increased computational power and time due to the additional nodes.

### 3D or Solids Elements

Solid Elements are used for complex load cases where out of plane effects need to be included in the analysis. Due to their increased computation demand, Solid Elements are only used when absolutely needed.

#### Tetrahedral – TET4 & TET10 Elements

Tetrahedral elements have similar disadvantages as 2D triangle elements, they can be too stiff. However, in comparison to Hexahedron elements, when they do provide accurate enough solutions they require far less computational power due to having half the number of nodal points.

#### Hexahedron – HEX8 & HEX20 Elements

Hexahedron elements provide excellent accuracy when they are required. Being the most demanding element type on this list they should be used sparingly if you want results in a reasonable amount of time. However, when out of plane effects can control an analysis they offer valuable insight that over elements do not.

### Additional FEA Elements

Today’s most advanced FEA plateforms have an abundance of element types to provide accurate results and optimize computational power requirements.

#### All ANSYS Element Types

In ANSYS previously mentioned element types form Femgen groups in which there are an abundant number of element types.

##### ANSYS Beam Type Elements

- Femgen – BE2
- 1 – BEAM3
- 2 – BEAM4
- 3 – BEAM23
- 4 – BEAM24
- 5 – BEAM44
- 6 – BEAM54
- 7 – PIPE16
- 8 – PIPE18
- 9 – PIPE20
- 10 – PIPE59
- 11 – PIPE60
- 12 – LINK1
- 13 – LINK8
- 14 – LINK10
- 15 – LINK11
- 16 – LINK31
- 17 – LINK32
- 18 – LINK33
- 19 – LINK34
- 20 – LINK68
- 21 – SHELL51
- 22 – SHELL61
- 23 – FLUID38
- 24 – FLUID66
- 25 – CONTAC12
- 26 – CONTAC52
- 27 – COMBIN14
- 28 – COMBIN39
- 29 – COMBIN40
- 30 – SURF19

- Femgen – BE3
- 1 – SURF19

##### ANSYS Plate/Shell Type Elements

- Femgen – TR3
- 1 – PLANE42
- 2 – PLANE13
- 3 – PLANE25
- 4 – PLANE55
- 5 – PLANE67
- 6 – PLANE75
- 7 – SHELL63
- 8 – SHELL41
- 9 – SHELL43
- 10 – SHELL57
- 11 – FLUID29
- 12 – HYPER56
- 13 – VISCO106

- Femgen – QU4
- 1 – PLANE42

- 2 – PLANE13
- 3 – PLANE25
- 4 – PLANE55
- 5 – PLANE67
- 6 – PLANE75
- 7 – SHELL63
- 8 – SHELL28
- 9 – SHELL41
- 10 – SHELL43
- 11 – SHELL57
- 12 – FLUID29
- 13 – FLUID79
- 14 – FLUID81
- 15 – HYPER56
- 16 – VISCO106
- 17 – SURF22
- 18 – FLUID15

- Femgen – TR6
- 1 – PLANE42
- 2 – PLANE35
- 3 – PLANE82
- 4 – PLANE53
- 5 – PLANE77
- 6 – PLANE78
- 7 – PLANE83
- 8 – SHELL93
- 9 – SHELL91
- 10 – SHELL99
- 11 – HYPER74
- 12 – HYPER84
- 13 – VISCO88
- 14 – VISCO108

- Femgen – QU8
- 1 – PLANE82
- 2 – PLANE53
- 3 – PLANE77
- 4 – PLANE78
- 5 – PLANE83
- 6 – SHELL93
- 7 – SHELL91
- 8 – SHELL99
- 9 – HYPER74
- 10 – HYPER84
- 11 – VISCO88
- 12 – VISCO108
- 13 – SURF22

##### ANSYS Brick Type Elements (Solids)

- Femgen – PE6
- 1 – SOLID45
- 2 – SOLID5
- 3 – SOLID46
- 4 – SOLID64
- 5 – SOLID65
- 6 – SOLID69
- 7 – SOLID70
- 8 – SOLID73
- 9 – SOLID96
- 10 – FLUID30
- 11 – HYPER58
- 12 – HYPER86
- 13 – VISCO107

- Femgen – HE8
- 1 – SOLID45
- 2 – SOLID5
- 3 – SOLID46
- 4 – SOLID64
- 5 – SOLID65
- 6 – SOLID69
- 7 – SOLID70
- 8 – SOLID73
- 9 – SOLID96
- 10 – FLUID30
- 11 – FLUID80
- 12 – HYPER58
- 13 – HYPER86
- 14 – VISCO107

- Femgen – PE15
- 1 – SOLID95
- 2 – SOLID90

- Femgen – HE20
- 1 – SOLID95
- 2 – SOLID90

##### ANSYS Point Type Elements

- Femgen – P-EL
- 1 – MASS21
- 2 – MASS71

As you can see from the previous list of all the element types in ANSYS, once you get into more advanced FEA software platforms there are countless types.

#### Using Only Higher Order Elements

You may have also noticed that ANSYS does not incorporate first order elements such as BEAM2 which is done to increase accuracy among solutions. In fact ANSYS doesn’t stop at just BEAM3, it goes up to BEAM4. BEAM23 and BEAM24 and higher are used for 3D beam applications.

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## FAQs

### WHAT IS elements and nodes in mesh? ›

What are FEA Nodes & Elements? **Elements are made up of at least 2 nodes.** **Nodes are points at which exact solutions are calculated**. Between nodes of a single element solutions are estimated through using interpolation.

### What are nodes in meshing? ›

A node is **a coordinate location in space where the degrees of freedom (DOFs) are defined**. The DOFs for this point represent the possible movement of this point due to the loading of the structure. The DOFs also represent which forces and moments are transferred from one element to the next.

### Which mesh type is best in FEA? ›

**Hex or “brick” elements** generally result in more accurate results at lower element counts than tet elements. If it is a complex geometry, tet elements may be the best choice.

### How does FEA determine mesh size? ›

FEA Mesh Sensitivity Study

The most scientific approach for determining the mesh resolution needed to obtain accurate results is to perform a mesh sensitivity study. To do this, simply **run your model with several different mesh sizes and plot the resulting stress or displacement values**.

### What is difference between element and node? ›

An element is a specific type of node, one that can be directly specified in the HTML with an HTML tag and can have properties like an id or a class. can have children, etc. Nodes vs Elements: **Nodes are all the different components that a webpage is made up of and elements are one type of node**.

### What are the different types of nodes? ›

**Originating node and execution node**. **Execution node and the destination node**.

### How many nodes are in 2D elements? ›

2D elements are **three- or four**-node elements that must be formulated in the YZ plane. They are used to model and analyze objects such as bearings or seals, or structures such as dams.

### What is mesh element? ›

The basic 3-dimensional element are the **tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron**. They all have triangular and quadrilateral faces. Extruded 2-dimensional models may be represented entirely by the prisms and hexahedra as extruded triangles and quadrilaterals.

### What are the types of elements used in FEA? ›

Elements in FEA are generally grouped into **1D element, 2D element, and 3D element**.

### Which type of meshing is best? ›

**Quadratic order meshing** might be more accurate than linear order meshing. Checking Orthogonal quality of elements (higher the better) and skewness of elements is necessary before proceeding for solution iterations.

### How many types of mesh are there? ›

The **three** types of meshing models are as follows: Tetrahedral - tetrahedral cell shape based core mesh. Polyhedral - polyhedral cell shape based core mesh.

### Which types of meshing we use? ›

There are two main types of meshing methods. For these purposes, we are referring to 3D models: **Tetrahedal element meshing or “tet”** **Hexahedral element meshing or “hex”**

### How do you know if mesh is good? ›

The most basic and accurate way to evaluate mesh quality is to **refine the mesh until a critical result such as the maximum stress in a specific location converges**: meaning that it doesn't change significantly as the mesh is a refinement.

### Why meshing is done in FEA? ›

Why is meshing important? Meshing is one of the key components **to obtaining accurate results from an FEA model**. The elements in the mesh must take many aspects into account to be able to discretize stress gradients accurately.

### How can I make FEA more accurate? ›

The key to generating effective FEA meshes is to **strike an appropriate balance between order and size for the particular problem that is being analyzed**. When possible, use second-order elements and iteratively refine the mesh until the results converge.

### What is node used for? ›

Node **allows developers to write JavaScript code that runs directly in a computer process itself instead of in a browser**. Node can, therefore, be used to write server-side applications with access to the operating system, file system, and everything else required to build fully-functional applications.

### Is Div an element or node? ›

The html tag is constructed by its children, head and body , and so on. **The div node is an element node**, while its child node ( Hello ) is a text node. The following table taken from MDN shows the popular node types: Node.

### How do you find the node of an element? ›

**To retrieve the text value of an element, you must retrieve the value of the elements' text node.**

- The getElementsByTagName Method. ...
- The ChildNodes Property. ...
- The nodeValue Property. ...
- Get an Attribute Value - getAttribute() ...
- Get an Attribute Value - getAttributeNode()

### What are the four types of nodes? ›

**The following node types are recognized:**

- technical root node (see Section 1, "The technical root node"),
- atomic nodes (see Section 2, "Atomic nodes"),
- paratactic structure root nodes (see Section 3, "Paratactic structure root nodes"),
- list structure root nodes (see Section 4, "List structure root nodes"),

### How do you find the number of nodes? ›

Angular nodes are usually equal to the azimuthal quantum number (l). The number of angular nodes = l The number of radial nodes = (n – l – 1) Total number of nodes = **n – 1**.

### How many node types are there in total? ›

1. How many node types are there in total? Explanation: There are total of **12** node types. The nodeType property returns the node type, as a number, of the specified node.

### Is 0D an element type or not? ›

**0D elements are commonly known as point elements**. In this example, the W shape has a center of gravity, and with a 0D element, I can represent the W shape as a point of mass. Other types of point elements include: Grounded spring, grounded damper, and grounded bush. 1D elements are commonly known as line elements.

### What is 3D element in FEA? ›

**A three-dimensional (3D) solid element is the most general finite element because all the displacement variables are dependent in x _{1}, x _{2} and x _{3} coordinates**. The formulation of 3D solids elements is straightforward, because it is basically an extension of 2D solids elements.

### What is 1D meshing? ›

1D element meshing is **the division of the member into multiple segments**, this does not affect the overall result but more segments allows smoother and better visualization of the results. 2D and 3D elements present similar traits in terms of meshing.

### How do you choose a mesh? ›

**Choosing a suitable mesh size**

- Perform chosen analysis for several different mesh sizes.
- Notice where high deformations or high stresses occur, perhaps it is worth to refine mesh in those regions.
- Collect data from analysis of each mesh: outcome, number of nodes in the model, computing time.

### What is element size in meshing? ›

The mesh size is defined by **the number of openings across one linear inch of screen**.

### What is the purpose of mesh in Ansys? ›

Ansys meshing capabilities **help reduce the amount of time and effort spent to get to accurate results**. Since meshing typically consumes a significant portion of the time it takes to get simulation results, Ansys helps by making better and more automated meshing tools.

### What are the 3 main types of elements? ›

The three major groups on the Periodic Table are the **metals, nonmetals and metalloids**. Elements within each group have similar physical and chemical properties.

### What are the minimum nodes in 2D elements? ›

2D elements are **3- or 4-node** isoparametric triangles or quadrilaterals which must be input in the global Y-Z plane.

### What are 2D shell elements in FEA? ›

Two Dimensional (2D) Elements, also commonly known as planar / shell elements are used in Finite Element Analysis (FEA) problems that predominately consist of thin or sheet based structures that the 2D plane's dimensions are very large in comparison to the 3^{rd} dimension, expected failure to be of bending deformation ...

### How do you improve mesh quality? ›

**5 Tips on How To Create a Better Mesh**

- A Simplified and Clean Watertight Geometry. ...
- Deciding and Maintaining a Good General Grid Size. ...
- Increasing Mesh Fineness at Critical Areas. ...
- Boundary-Layer Refinement and Y+ ...
- Mesh Convergence Study.

### What is mesh and its types? ›

Mesh Type | Geometry | Topology |
---|---|---|

Rectilinear Mesh | semi-implicit | implicit |

Uniform Mesh | implicit | implicit |

Unstructured Mesh | explicit | explicit |

Particle Mesh | explicit | implicit |

### Which meshing type gives more accurate solution? ›

Typically, **finer meshes with smaller elements** produce more accurate results. However, finer meshes take longer to solve. However, there is a point where the mesh is refined enough to accurately capture the results.

### What material is mesh? ›

Mesh fabric is fabricated most commonly from **stainless steel, copper, bronze, polyester (or nylon) and polypropylene**. As the fibers are woven together, they create a very flexible, net-type finish that has a tremendous range of end-uses.

### What are mesh properties? ›

Fabric breathability | Very breathable |

Moisture-wicking abilities | Medium |

Heat retention abilities | Low |

Stretch ability (give) | High |

Prone to pilling/bubbling | None |

### What is 2D mesh? ›

2D Meshing. **A surface mesh or "shell mesh" represents model parts that are relatively two-dimensional, such as sheet metal or a hollow plastic cowl or case**. 2D Elements. Supported 2D elements. Automatic Meshing.

### What are the steps in FEA? ›

**A Step By Step Introduction to FEA**

- Step 1 – Create a solid model of the object. ...
- Step 2 – Check the Drawing. ...
- Step 3 – Mesh the model. ...
- Step 4 – Apply Loads and Restraints. ...
- Step 5 – Run the Model with 2 Quality Checks. ...
- Step 6 – Quality Check – Displacement Plots. ...
- Step 7 – Stress Results. ...
- Step 8 – The Report.

### What is mesh generation in FEM? ›

Mesh generation is **the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells**. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain.

### What is the difference between tetrahedral and hexahedral mesh? ›

Key Takeaways. A tetrahedral mesh is a standard tool used to generate structured and unstructured meshes. **One alternative to a tetrahedral mesh is to use a hexahedral mesh**. Although cubic meshes are technically hexahedral, arbitrary hexahedral meshes can be used to build less computationally intensive simulation models ...

### What is an element in Ansys? ›

**Element types are defined in the input file with ANSYS 'ET' commands**. The element type number is assigned by the interface program. The same element type can be defined twice with two different numbers if its material or/and physical properties are different from one to the other.

### What is node in mesh Ansys? ›

Nodes are **the intersection points between mesh elements that are created to solve FEA problems**. If you select the selection option that is shown by the red arrow above, you can select the nodes by clicking with your mouse on the graphics window in ANSYS® Mechanical.

### What is nodes in Ansys? ›

A node is simply **a point in space, defined by its coordinates, at which DEGREES OF FREEDOM are defined**. In finite element analysis a degree of freedom can take many forms, but depends on the type of analysis being performed.

### What is a truss element? ›

Truss elements are **two-node members which allow arbitrary orientation in the XYZ coordinate system**. The truss transmits axial force only and, in general, is a three degree-of-freedom (DOF) element. Trusses are used to model structures such as towers, bridges, and buildings.

### What are the types of elements used in FEA? ›

Elements in FEA are generally grouped into **1D element, 2D element, and 3D element**.

### What is mesh element? ›

The basic 3-dimensional element are the **tetrahedron, quadrilateral pyramid, triangular prism, and hexahedron**. They all have triangular and quadrilateral faces. Extruded 2-dimensional models may be represented entirely by the prisms and hexahedra as extruded triangles and quadrilaterals.

### How do you count nodes in Ansys? ›

I think a shortcut for it is to **use the command *vget**, in ansys, you can read about it in the help, it is very versatile command for storing array data of almost any kind in ansys, including the node numbers of selected elements. The magic keyword "count" works amazing!

### How many nodes are in 2D elements? ›

2D elements are **three- or four**-node elements that must be formulated in the YZ plane. They are used to model and analyze objects such as bearings or seals, or structures such as dams.

### What is the difference between key points and nodes in Ansys? ›

**A point refers to the intersection of two or more (geometry) lines. .** **A mesh node ('node' for short) refers to the intersection of two ore more mesh lines**.

### What are the minimum nodes in 2D elements? ›

2D elements are **3- or 4-node** isoparametric triangles or quadrilaterals which must be input in the global Y-Z plane.

### What are the main steps involved in FEA? ›

**A Step By Step Introduction to FEA**

- Step 1 – Create a solid model of the object. ...
- Step 2 – Check the Drawing. ...
- Step 3 – Mesh the model. ...
- Step 4 – Apply Loads and Restraints. ...
- Step 5 – Run the Model with 2 Quality Checks. ...
- Step 6 – Quality Check – Displacement Plots. ...
- Step 7 – Stress Results. ...
- Step 8 – The Report.

### Why do people do meshing in Ansys? ›

Ansys meshing capabilities **help reduce the amount of time and effort spent to get to accurate results**. Since meshing typically consumes a significant portion of the time it takes to get simulation results, Ansys helps by making better and more automated meshing tools.

### What is a primary node? ›

The primary node is **the node in the BeyondTrust cluster that is configured as the primary site in failover**. The network in which the primary lives should be a central location in relation to your network as a whole.

### What is stiffness matrix in FEA? ›

The stiffness matrix is **the n-element square matrix A defined by**. **By defining the vector F with components**. **, the coefficients u _{i} are determined by the linear system Au = F**. The stiffness matrix is symmetric, i.e. A

_{ij}= A

_{ji}, so all its eigenvalues are real.

### What is a bar element? ›

The linear bar element is **a one-dimensional finite element where the local and global coordinates coincide**. It is characterized by linear shape functions and is identical to the spring element except that the stiffness of the bar is not given directly.

### Is truss 1D or 2d element? ›

2.1. 1 Truss **1D element**

Represents linear isoparametric truss element in 1D. The elements are assumed to be located along the x-axis.