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Engineering Analysis Nomenclature| Intro To FEA

There are a lot Analysis types for FEA. In order to gain insight into the performance of your product you need to understand which analysis type suits your needs.

Common Analysis Nomenclature

Linear

Linear Analysis assumes that the structure’s behavior obey’s Hooke’s Law. This means that the forces are linearly proportional to deformation in other words if you double the load (force) then the deformation will also double.

Examples of when not to use:

  • When plastic deformation occurs or is expected. If the maximum stress experienced by the part is greater than it’s yield stress.
  • When strain hardening occurs.
  • When the Boundary Conditions change during the application of load.
  • Materials that do not act elastically.

Nonlinear

Nonlinear analysis should be used when a part experiences plastic deformation. If a structure is also expected to experience significant displacement, then nonlinear analysis should be considered. Nonlinear analysis also has the advantage of being able to model strain hardening if you provide the correct material properties. Incorporating strain hardening into your analysis can greatly improve the analysis accuracy and predict the part surviving loading while linear analysis would have predicted failure.

Static

A load is static if the magnitude and direction to not change in respect to time. Loads have to be applied slowly and gradually until they reach their full magnitudes.

Examples of when not to use:

  • When vibration loads are present such as during an earthquake or from rotating parts.
  • When a load rapidly changes in magnitude such as during a vehicle crash or a bullet impact.
  • When analyzing damping or inertial properties.

Dynamic

Dynamic analysis is used to when a part experiences loading which changes with time. Loading can be sinusoidal (cyclical) such as in vibration loading or rotor-dynamics. Dynamic loads also include impact loads such as drop analysis, or crash analysis. Dynamic analysis may be used to determine damping or inertial properties, structural properties, natural frequencies or modes, and more.

Steady State

Steady State Analysis is used for a system that is in equilibrium. For instance when you load an existing building with additional dead load (structure and immovable fixtures), initially the structure experiences a transient load as it begins to strain under the new load. However, after enough time has passed, the structures reaction will stop changing and the stress and stress will remain constant, at this point the structure is in a steady state.

Transient

Transient Analysis is similar to Dynamic analysis in which the loading changes with respect to time. Transient analysis is used to model impact loading reactions. Since everything acts like partially like a spring when you impact a structure with force there is a reaction which causes a dampening sinusoidal loading of the structure. For instance if you hit a gong with a mallet you will induce vibration into the gong which causes it to ring. Overtime the vibration’s amplitude decreases and the frequency increases until the gong returns to a steady state at which it is silent again. The reaction of the gong to the mallet may be analyzed using a transient analysis.

Normal Modes (Aka Modal Analysis)

Normal Modes of a system is the frequency at which all parts of the system are vibration at the same frequency with a fixed phase relation, also known as resonance frequency. Normal modes occur at fixed frequencies for a system. Using normal mode (aka modal) analysis you can determine these frequency points.

Prestress

Prestress occurs when a system is stressed in accordance with its design prior to receiving its service load. This is very helpful for materials that react significantly different under different types of load. For example a cable may be prestressed in tension to prevent it from ever going into compression which it cannot carry. Concrete is commonly prestressed in compression so that it never crosses into tension stress which it simply cracks. Prestress loading needs to be considered during the analysis to accurately analyze a design.

Residual Stress

Residual stresses occur when a solid has stresses which remain after the applied load is relaxed. This is commonly taken advantage of in engineering through the use of heat treatment, and cold forming & hardening where the materials crystalline structure can be manipulated to increase strength. It also commonly occurs in welding when local heat cause warping due to local expansion. If residual stresses aren’t factored in during an analysis it can lead to premature failure of a part, this is why best welding practices are critical to adhere to.

Direct Frequency

Direct frequency analysis is used to analyze the steady-state response of a sinusoidal load applied at a single frequency. This is commonly used for rotordynamics or the analysis of rotating structures at a constant rpm.

Random Response

Random Response Analysis is used when the loading of a system is nondeterministic and can only be characterized statistically. For instance over the entire design life of a structure it may be subject to many reoccurring loading scenarios. While each individual loading scenario may be simple to design for, the problem comes when the sum of all the loading scenarios is considered. After a lifetime of repeated and random loads a structure may fail due to fatigue. In order to predict the lifespan of a structure statistics along with conservative safety factors are used to determine the frequency of different loading scenarios. When this is combined with random response analysis it can be used to determine a cycle life and therefore a lifespan of a structure. This is commonly used for seismic and wind loads of structures, to design the frame and suspension of a car, and more.

Fatigue

Fatigue occurs overtime as a structure is subject to loads. While a structure may have no trouble withstanding the first loading, after repeated loading the sum of all wear can lead to a fatigue failure. In engineering there are two common types, low cycle fatigue and high cycle fatigue. Low cycle fatigue leads to failure after just a few load cycles. Low cycle fatigue is common when a component only needs to be loaded once such as a bolt. High cycle fatigue looks at thousands of load cycles and is common for components such as a cars suspension.

Thermal or Heat Transfer

Thermal or heat transfer occurs when a high temperature body transfers thermal energy to a lower temperature body. In engineering analysis thermal transfer and thermal loads effect operating efficiency, thermal expansion, material strength, and more.


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Finite Element Method

FEA Mesh Elements & Nodes Guide | Intro to FEA

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?

2 Node Line Element - FEA
Simplest Element
2-Node Single Element

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

FEA - Smaller Elements
Half Size Elements
2-Node Half Size Elements

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

3 Node Element
3-Node Quadratic Interpolation 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

FEA 2D Elements-1
FEA- 2D Elements-2

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.


ASR is a mechanical and aerospace engineering firm that specializes in engineering design and analysis including advanced FEA & CFD. If you are in need of engineering services then contact us today to speak to one of our experienced engineers for a free quote on your project!