*Finite element analysis (FEA) is defined as the process of using mathematical calculations, models, and simulations to understand, analyze, and predict the behavior of an object, part, assembly, or structure under various physical conditions. This article explains finite element analysis in detail, how it works, its uses, and some of the known software that enables FEA.*

### Table of Contents

## What Is Finite Element Analysis?

**Finite element analysis (FEA) refers to the process of using mathematical calculations, models, and simulations to understand, analyze, and predict the behavior of an object, part, assembly, or structure under various physical conditions. FEA is typically used by engineers to model physical forces that help them identify vulnerabilities in the design of their product prototypes. It allows them to localize the design problems and optimize the components, thereby streamlining the design phase of the product. Potential design issues may refer to identifying overheating parts, weak spots, or areas of tension.**

Technically, FEA uses the finite element method (FEM) to break down the structure of an object into multiple elements and manageable portions, which are later reconnected through points called nodes. FEM generates a series of algebraic equations that engineers, scientists, developers, and designers can use to perform the FEA of any structure.

In the mathematical context, the physical features of a product such as structural appearance, fluid behavior, or thermal coefficient are best illustrated by employing partial differential equations (PDEs). The emergence of FEA enabled computers and machines to find solutions for linear and nonlinear PDEs. Although FEA offers a numerical approach to handling PDEs, these are only capable of finding approximate results.

FEA significantly reduced the number of experiments performed and prototypes created that are necessary to optimize the design of product components. Mathematical papers that showed signs of FEA techniques first appeared in Schellbach’s work in 1851. In the mid-1950s, FEA development was still in its infancy stage; however, efforts were being made to realize real-world applications through it. In the 1970s, programs such as ABAQUS, ADINA, and ANSYS paved the way for efficient FEA strategies.

Later, engineers from different industries fine-tuned the FEA math and evolved it further to solve several structural mechanics problems, typically benefitting the civil engineering and aerospace sectors. Today, FEA is a key component of the product development cycle with facilities for virtual testing and design optimization that not only improve the quality of the product but also speed up the process of delivering a product to the market.

Finite element analysis is broadly classified into the following types:

### 1. Engineering seismic calculations

Seismic analysis is used to study the performance of a structure at different locations where significant variations in ground frequencies and vibrations exist. The analysis helps determine whether the structure is sturdy enough to withstand conditions at different geographic places.

### 2. Linear static analysis

This defines the type of FEA where scaled models are analyzed by applying linear proportions. This implies that if a structure performs well at a small scale, employing linear proportions the full-scale version of the structure should perform exactly the way the small-scale version does.

### 3. Modal analysis

Everything in existence vibrates at its own fundamental frequency. Hence, as more and more objects are added to a structure, outside factors such as wind speed tend to influence the structure’s vibrations immensely. To understand these phenomena, modal analysis is employed where different forced vibrations are applied to structures that can affect it in several ways. Thus, such analysis allows one to make subtle adjustments to the structure in the design phase itself based on the vibrations that the structure can withstand.

### 4. Thermal engineering analysis

It is a well-known fact that both heat and cold can substantially affect the design of any structure. Thermal engineering analysis studies how temperature variation impacts a structure.

### 5. Fluid dynamic calculations

This FEA type is typically beneficial for the oil & gas industry where fluids or gasses are in continuous random motion. Moreover, as oils & gases have varying density and flow, they can significantly impact the structural level.

Thus, with fluid dynamic analysis, one can make corresponding changes to the structure based on the impact of flowing oil or gas through a pipeline or tube.

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## How Does Finite Element Analysis Work?

Finite element analysis is an intricate and complex mathematical process. FEA simulations are conducted via specialized software with results being displayed on a computer-generated â€˜color scale’ for the visualization of data.

Fundamentally, FEA begins by breaking down large structures into smaller and manageable units. The more you understand the smaller components, the better position you are in to predict how larger and complicated structures may respond to any external stresses and strains.

FEA involves three steps: preprocess, process, and post-process. In the first step, the structure is broken down into tinier elements by using FEM, and the simulation is set up. For example, consider the structure of a bar. It is initially split into multiple smaller pieces such as simple triangles or cubes to help better define the model parameters. Moreover, such FEM-based simulations can be accelerated by employing machine learning models.

Upon breakdown, the position for the placement of nodes is defined for the 2D or 3D rendering of the structural design. Once the nodal points are selected, the nodes are connected by drawing lines, thereby creating a mesh structure, which reveals the final shape of the design. The mesh structure encompasses the finite set of elements that constitute the structure, wherein, every element amongst the set can be represented by a set of matrices. When several such elements are connected, the individual matrices are compiled into a single structural matrix. The name â€˜finite element analysis’ is thus derived.

With the focus on a mesh structure, you can handle its mini sections with ease. And by doing so, you can figure out the response of the entire structure when it encounters similar circumstances. It is important to note here that the denser the mesh structure, the more precise and accurate the results will be. Meshing basically stabilizes the analysis performance and also provides reliable result approximations. However, with the addition of nodal points or elements to the mesh, the subsequent increase in computational complexity is encountered.

In the final post-processing step, the generated output variables are analyzed, organized, and presented for interpretation. Moreover, the results are displayed in a user-friendly or understandable manner where the team of FEA solvers use sorting and charting techniques such as bar charting, point & figure charting, or equal tick charts for the efficient visualization of finite elements.

The finite element analysis workflow involves the following steps:

1. Create a geometry â€“ Define geometry of a structure or object.

2. Pre-process:

1. Meshing â€“ Create mesh structure based on structure’s geometry.

2. Set boundary conditions â€“ Assign boundary, load, and initial conditions for the structure.

3. Process:

1. Numerical analysis â€“ Perform numerical analysis of smaller mesh elements.

4. Post-process:

1. Post-process results â€“ Organize and illustrate results for effective interpretation.

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## Uses of Finite Element Analysis

Finite element analysis is used across all core industries, including aerospace, industrial engineering, manufacturing, dentistry, biomechanical research, CFD, and plenty of others, mainly for the following reasons:

### 1. Offers digital prototyping

Creating a physical prototype to determine the stresses that the real world exerts and how objects react to them can be an expensive process. Instead, FEA allows you to develop a digital model for the object and study the stresses it encounters in the real world.

### 2. Provides easy visualization

With FEA, you can model the interior and exterior of an object, thereby allowing you to point out design flaws that are vulnerable to external conditions. As such, users can correct such design problems through finite element analysis that enables the visualization of stresses, strains, and thermal variations.

### 3. Applies boundary conditions

FEA allows you to study how the developed digital prototype responds to boundary conditions such as external forces, thermal effects, applied heat, and positional constraints.

### 4. Accurate object modeling

FEA software-based simulation models are far more accurate than physical models that are developed manually. This is why FEA has been the preferred option for most engineers, designers, and others.

Let’s understand how FEA is specifically used by each industry.

**1. Automotive industry:** In the automotive industry, FEA software is used for various applications such as assessing the design components of an automobile, including the brakes, suspensions, bonnet, or other bodywork. Moreover, it also helps in carrying out virtual crash tests to better understand the performance of the vehicle design in a simulated crash-like situation.

**2. Civil engineering: **FEA techniques are used to check the response of structures such as buildings, roads, and bridges to various topographical and environmental conditions. It allows you to design complex structures with complete safety.

**3. Industrial equipment**: FEA is essential in designing and building durable industrial equipment such as tanks, pipes, etc. It allows you to predict how external heat pressure can deform tanks, pipes, or vessels, and how much force such equipment can endure to stay intact without getting affected.

**4. Manufacturing industry**: In the manufacturing sector, FEA software allows designers to get a sneak-peak into the future performance and behavior of components such as metals before developing prototypes. Such a practice saves businesses from investing their time, effort, money, and resources in ineffective product designs. With finite element analysis, you can forecast whether the designed part will remain free from fractures or physical damage in the foreseeable future. The approach helps companies improve their ROI, shorten design cycles, reduce design costs, and boost overall design productivity.

**5. Aerospace industry**: The aerospace industry uses FEA primarily for structural analysis. It is used for studying the aero-servo-elastic stability of aircraft, analyzing aircraft shapes, and determining the natural vibrational frequencies of aircraft components. Moreover, FEA also helps forecast and analyze aircraft behavior or reaction to structural deformity and thermal loads.

**6. Biomechanical research**: Finite element analysis is a handy tool to reconstruct complex geometrical structures such as the natural and artificial tissues of humans. As FEA relies on mathematical functions and calculations, it aids in developing a complete understanding of craniofacial biomechanics and its analysis.

**7. Dentistry**: FEA helps in simulating the geometry and surface structure of dental implants. It allows you to understand the material features of the implant, jawbone, and implant-jawbone interface. This analysis method is key to determining the success and failure of dental implants in clinical conditions. Moreover, users can also employ advanced image techniques to learn the effect of the applied mechanical forces on living bone tissues and their subsequent responses.

FEA helps in detailing the stress patterns that dental or bone implants can suffer in the future. This knowledge allows the development of sturdy implant designs and identifying the correct positions for their placement.

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## Finite Element Analysis Software

The global finite element analysis software market has grown exponentially over the years. Innovation in science & technology and engineering and increased investments in research and development by companies worldwide have played a key role in such spectacular market growth.

According to an August 2022 report by Research Nester, revenue generated by the FEA software market stood at $5 billion in 2021, which is expected to climb to $12 billion by 2031, expanding at a CAGR of around 10%. Moreover, as per the report, ANSYS, Inc., Synopsys, Inc., Autodesk, Inc., Dassault SystÃ¨mes, and IBM Corporation are key players in the FEA software market.

Let’s look at some of the top finite element analysis software in 2022.

### 1. ANSYS

ANSYS is a popular FEA software that is extensively used in the engineering space. The software embeds several modules capable of simulating various physical aspects such as fluids (in CFX and FLUENT), static/dynamic motion analyses, thermal/structural analyses, and modal analyses for determining vibrational frequencies. ANSYS FLUENT works with 2D mesh, while CFX uses tetra and hexa mesh structures (3D). All these modules are combined under the ANSYS framework, offering a comprehensive toolset to study multiple physical factors.

Today, ANSYS uses AI and ML methods for dynamically determining simulation parameters. Such practices contribute immensely to speeding up the product design optimization process by analyzing thousands of parameters in no time. As a result, companies see a boost in their business intelligence strategies as it tends to improve the speed and accuracy of product design.

### 2. SimScale

SimScale is a cloud-based FEA software that serves as an alternative to ANSYS. It consists of three essential modules for thermal analyses, computational fluid dynamics (CFD), and mechanical analyses, such as static/dynamic analyses, vibrational analyses, etc.

Researchers around the world use SimScale to study various complex physical systems. This includes the analysis of planetary mergers or even factors that influence climate on the Earth. The software generates high-quality maps and topographical illustrations, making it suitable for geological research and climate modeling.

### 3. Autodesk

Autodesk is a well-known engineering software, primarily because of its two units: AutoCAD and Inventor software. AutoCAD is computer-aided design software widely used to create 2D and 3D drawings. Autodesk Inventor is a design application used to create 3D mechanical designs, perform simulations, and visualize and document tasks. Autodesk also offers a CFD module for fluid system analyses.

### 4. ABAQUS

ABAQUS is a competitor of ANSYS software. It provides five specific tools for its users: Complete Abaqus Environment (CAE) for mechanical units and assemblies, Abaqus Standard for static/low-speed dynamic stresses, Abaqus Explicit for non-linear and transient FEA analysis such as automotive crashworthiness, Abaqus CFD for fluid analyses, and Abaqus Electromagnetics, which is well-suited for electronic and electromagnetic studies.

### 5. OpenFOAM

OpenFOAM is a finite element analysis software that offers cost-effective methods to design, test, and fabricate mechanical & electronic systems. The software is typically designed to maximize the performance of systems operating in the oil & gas industry. It is used by engineers, chemists, and oil & gas commission (OGC) consultants for better decision-making.

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### Takeaway

Finite element analysis provides engineers, manufacturers, and designers with multiple ways to speed up their core operations and simplify their workers’ day-to-day jobs. FEA is vital for industries as it cuts down on design and manufacturing costs, speeds up design processes, optimizes designs by evaluating alternative material designs, and reduces unnecessary material waste. Whether in the automotive, manufacturing, aerospace, or energy sector, finite element analysis provides safe, sturdy, and durable designs.

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