What is Finite Element Analysis (FEA)?

Finite element analysis (FEA) is the process of predicting an object’s behavior based on calculations made with the finite element method (FEM). While FEM is a mathematical technique, FEA is the interpretation of the results FEM provides. FEA gives engineers insights into complex systems and structures, helping them make more informed design decisions. 

FEM uses math to break complex systems into smaller, simpler pieces, or “elements.” It then applies differential equations to each element individually, using the power of computers to divide, then conquer engineering problems.  

FEA is the application of FEM equations and is the basis of many types of simulation software. It’s used to validate and test designs safely, quickly, and economically by creating virtual models of real-world assets.

Finite element modeling makes it possible to simulate the physical world without the expense, time, or risk of building physical prototypes. These models are used to solve for various conditions and scenarios across a variety of industries, especially those with complex or high-risk environments such as aerospace and biomechanics. 

The chair you’re sitting on. Your wireless phone charger. The blood flowing through your veins. All around us there are objects and systems that can be modeled using FEA. With its ability to approximate highly irregular dimensional problems, FEA can be applied to just about everything. Any physical behavior described using differential equations, like most engineering problems and even certain esoteric problems like quantum mechanics, can be solved using FEA.

FEA is commonly used in industries where physical testing is impossible or impractical. Examples of applications using FEA models include:

Civil Engineering: FEA is used to evaluate the safety and integrity of structures such as bridges, buildings, and dams. FEA can help engineers optimize their designs to meet safety standards and predict maintenance needs. 

Aerospace Engineering: FEA is used to simulate the performance of aircraft components and systems against many different flight conditions. Landing gear integrity, aerodynamics, thermal stress, fatigue life prediction, vibrations, fuel usage and more can be modeled using FEA.

Automotive Engineering: FEA is used to assess systems throughout a vehicle, including heads-up displays, battery longevity, exterior lighting, and structural crashworthiness. In safety tests, FEA can help engineers evaluate the performance of various safety systems under a variety of impact conditions.

Finite Element Analysis works by discretizing the domain of interest and then assembling physics equations to solve the engineering problem at hand.  By assembling these elements together to represent the physical system, engineers can predict the behavior of the whole structure. With FEA, answering the question, “Will my car be safe after being driven over 100,000 miles?” starts by dividing the car into systems, systems into components, and components into elements using a grid of elements, known as meshing. 

The Finite Element Analysis Process

1. Pre-process: Define the physics and real-world conditions to be used in the model.
   
2. Process: Divide the object into finite elements via meshing and apply the relevant physics representations and/or equations to each element. Then assemble the equations and solve them.
3. Post-process: Compute results to analyze and interpret implications for the whole domain.

Engineers face huge challenges in designing solutions that meet the evolving needs of people and planet. To explore unlimited scenarios and conditions, they rely on the flexibility of FEA. With FEA, it’s possible to model any shape geometry (from a square block to the human heart), at any size (from the nanoscale to a large passenger jet airplane ), with any type of physics (heat transfer, fluid dynamics, structural mechanics, etc.). Basically, as long as you have a partial differential equation, you can use FEA. 

FEA advantages include:

Assess complex geometries: FEA can analyze intricate structures that would otherwise be challenging or impossible to evaluate

Simulate a range of physics: FEA allows engineers to model multiple physics problems all at once

Save time, money and resources: FEA reduces the need for physical prototyping so engineers can evaluate the safety, reliability and performance of a design before it’s ever built

As with many technologies, the output is only as good as the input. FEA models depend on the accuracy of the information used to build them. All the assumptions, such as the geometry, the material properties, and the analysis type, can affect the integrity of the model’s results. Only by feeding accurate data in can FEA produce accurate insights out.

Another challenge of FEA is that for best results, it should be used in collaboration with experts . While FEA has become easier to use and AI promises to democratize simulation even further, there is currently still the need for appropriate guidance and safeguards to use FEA tools effectively.

Depending on the specific engineering problems being addressed, there are several types of tests that can be administered using FEA. Multi-purpose simulation software, such as Ansys Mechanical, provides a range of analysis tools to perform custom design scenarios. Some of the most common types of FEA tests are:

Static analysis: Performed on steady loads when conditions will not change over time.  

Dynamic analysis: Used for calculations involving variation over time or frequency.  

Modal analysis: Looks at natural frequencies to predict how structures vibrate and how those vibrations can affect performance. 

As the world faces increasingly more complex engineering problems, such as energy production, automation, and deep space travel, FEA will continue to be the right technique for exploring the most innovative solutions. By leveraging the ever-increasing processing power of High Performance Computing (HPC), and incorporating the cognitive perception of AI, FEA of the future will be able to provide better insights to more people, faster than ever. 

Related Resources