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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