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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