 # What is Finite Element Analysis (FEA) | Engineering Analysis

Finite element analysis (FEA) is the analysis or simulation of a phenomenon using the finite element method (FEM).

### FEA Benefits

FEA delivers significant advantages to engineers and designers including:

• Gaining a strong understanding of a design’s performance prior to prototyping.
• Optimizing a design for weight and cost while maintaining performance.
• Limiting the number of expensive prototypes needed prior to reaching a final product.
• Analyze why a design failed performance testing to allow for designing a solution
• Analyze and optimize complex geometries, composites, interactions, and loading scenarios that would otherwise require a guess test and revise approach to design.

## Understanding Finite Element Analysis (FEA)

While FEA is a powerful tool that engineers use to deliver exceptional designs, just as with any other tool it’s value is dependent upon a user who understands the limits of the underlying system. Without a strong understanding of how each input affects the computational model and the physics behind a phenomenon, FEA can provide a inaccurate results that hinder more than help. Prior to accepting FEA results an engineer should verify and validate the results using engineering judgement, and comparing to hand calculations and experimental data.

## Pre-processing

Pre-processing includes everything needed to fully define a model so that FEM’s discretization method can run properly and attain an accurate result.

### Boundary Conditions

With limited computational power, time, and budget FEA models aren’t able to incorporate every single element into a simulation. Instead, engineers use their judgment to define boundary conditions that best approximates a loading scenario in the simplest way possible. Boundary conditions include constraints and loads.

#### Constraints

Constraints are boundary conditions that represent physical characteristics such as connections, surfaces, and thermal boundaries. In other terms, constraints constrain a model either physically or thermally at defined nodes in the defined axis and rotation. Depending upon the FEA software package constraint names will vary, however, they generally consist of the following or similar.

• Structural
• Fixed
• No Translation
• No Rotation
• Free
• Pin
• Frictionless
• Response Spectrum
• Thermal

Loads are used to apply performance conditions to a model. similarly to constraints, loads are applied at user specified nodes. Depending upon the FEA software package load names will vary, however, they generally consist of the following or similar.

• Force
• Moment
• Pressure
• Gravity
• Remote Force
• Rotational Force
• Enforced Motion
• Initial Condition
• Body Temperature
• Temperature
• Convection
• Heat Generation
• Heat Flux

### FEA Mesh

FEA generates a mesh consisting of nodes and elements based on the supplied geometry and mesh definition. When the simulation is ran the results are determined only at the given nodes in order to simplify the problem to a finite number of results. Interpolation is then used to estimate the results between nodes. The accuracy of an analysis therefore is dependent upon the element size or the spacing between nodes. However, it is not advisable to always reduce the element size as doing so increases the computational requirement for a model while potentially returning negligible improvements in accuracy.

#### Automated Mesh vs User Defined Mesh

In order to save a significant amount of time while constructing your model, FEA packages allow you to set mesh rules which it will automatically apply to an entire model. However, in order to generate an accurate result and not require excessive computational time, you will want to go back and define local mesh rules. For instance, locations where stress concentrations are likely to occur, such as a bolt hole, or extreme edge of a part in bending you, will want to increase the mesh density by decreasing the element size manually.

### Analysis Types

#### Linear vs Non-linear

The analysis type you should choose depends upon your design, performance, and load scenario. For instance, if you have a simply supported beam (pin-frictionless) with all non-transient loads (don’t change with time) and minimal deformation then you want to apply a linear static analysis. However, if you take the same beam instead of having it be simply supported you make it cantilevered (fixed-free) and apply the same loads but now have significant deformation, then you will want to apply a nonlinear static analysis. As a structure deforms with load the moment changes which therefore requires running multiple iterations prior to converging to a solution.

#### Transient

Transient analysis is used when a load changes with time or if you are looking to cycle a product to determine it’s fatigue life. Transient analysis includes anything from impact loads to cyclical loading where work hardening or plastic deformation can occur which changes a structure’s response to loading.

Depending upon the FEA software package analysis type names will vary, however, they generally consist of the following or similar.

• Linear Static
• Normal Modes
• Linear Buckling
• Prestress Static
• Prestress Normal Modes
• Nonlinear Static
• Nonlinear Buckling
• Direct Transient Response
• Modal Transient Response
• Impact Analysis
• Nonlinear Transient Response
• Direct Frequency Response
• Modal Frequency Response
• Random Response
• Shock/Response Spectrum
• Multi-Axial Fatigue
• Vibration Fatigue
• Linear Steady State Heat Transfer
• Nonlinear Steady State Heat Transfer
• Nonlinear Transient Heat Transfer

### Solver | Uncovering the Blackbox

In order to understand what inputs into FEA are actually doing you need to understand the mathematical machine behind the software.

#### Governing Equations & Boundary Conditions

While solving an FEA model, it applies governing equations in combination with boundary conditions to determine the results at points within a domain.

#### Discretization

In order to simplify the problem, FEM uses discretization which reduces the problem from needing to find a solution at an infinite number locations throughout a domain to instead find a solution at only defined points or nodes within the domain. Once a solution is found at each node, FEM then interpolates along elements to approximate the result.

#### Element Interpolation

In order to improve the accuracy of the approximation of a result, quadratic interpolation is typically used instead of linear interpolation. In order to allow for quadratic interpolation, a 3rd node is placed on each element at the center. This is critical as most physical governing equations, which FEM is approximating while interpolating, are not linear and are instead quadratic.

### Post-Processing

Once a model has been solved you enter post-processing where the results can be analyzed for insight.

#### Result Types

FEA delivers a wide range of results including the following.

• Von Mises Stress
• 1st Principal Stress
• 3rd Principal Stress
• Displacement (Total, X, Y, Z)
• Safety Factor
• Stress (XX, XY, XZ, YY, YZ, ZZ)
• Strain
• Equivalent Strain
• 1st Principal Strain
• 3rd Principal Strain
• XX, XY, XZ, YY, YZ, ZZ
• Contact Pressure (Total, X, Y, Z)

#### Von Mises Stress

Von Mises Stress is typically the most critical component of your results. This shows the total stress at any given point of model. If you compare these results to the materials yield strength you can determine whether the section is within elastic or plastic deformation aka if it has yielded. Should the material being used undergo strain hardening after yielding and if a significant portion of the model is yielded then you will want to run a nonlinear analysis instead of a linear analysis.

#### 1st Principal Stress

1st principal helps with determining the tensile stress at a given location. This can be very helpful for materials such as concrete or masonry which typically crack immediately upon experience tensile stress.

#### 3rd Principal Stress

3rd principal stress helps with determining the compressive stress at a given location. This can be very helpful for tension structures such as cables which cannot go into compression.

#### Displacement

Displacement gives the total deformation of the model. If a model deforms significantly during an analysis be sure to use a nonlinear analysis instead of a linear analysis to allow for using an iterative solving process which incorporates changes in loading as a model deforms.