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by Snigdha Sarkar, September 22, 2022

What is Finite Element Analysis?

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Finite Element Analysis (FEA) is the use of partial differential equations to create a computerized simulation for predicting how a product will react when subjected to real-world forces using the finite element method. The finite element method is similar to computational fluid dynamics (CFD) analysis except instead of solving fluid-flow problems you are solving structural problems.

Vibration, heat, fluid flow, magnetics, acoustics, and other phenomena all take their toll. With FEA simulation, you can determine if your product will break, wear out, or operate as intended under these stresses. Hence, you can decide whether or not you should reconsider your product design.

Engineers at every experience level can use FEA software to solve complex engineering problems faster and more accurately. Unlike FEA systems of the past, today’s leading FEA packages like Ansys Mechanical are easy to use. They integrate seamlessly with CAD software, automate previously complicated workflows, and have intuitive and customizable user interfaces.

This article breaks down the basics of FEA, explains why it’s such a powerful technique and highlights its shortcomings. Read on to find out:

  • What Finite Element Analysis Is
  • What an FEA Workflow Looks Like
  • Limitations of FEA
  • Some Important Definitions
  • Why FEA Is Everywhere

finite-element-analysis

What is Finite Element Analysis?

The FEA process predicts what will happen to a product under a range of conditions. It breaks a physical object down into thousands of tiny elements and use an algebraic equation to calculate how each one will respond. You can think of these elements as little cubes or blocks, but they could be millions of triangles, hexahedrons, or tetrahedrons (…need I go on?) 

Once you connect up all of these granular elements (via nodes), you get a “global” view of how your product’s structural behavior will be affected by physical forces, including: 

  • Vibration
  • Electrostatics
  • Motion
  • Mechanical vibration
  • Fatigue
  • Plastic injection molding
  • Heat transfer
  • Mechanical stress
  • Fluid flow

FEA’s valuable insights enable the optimization of designs before manufacture. This is crucial, as changes made at the conception stage are frequently 1,000 times less costly than those made later down the line. Catching problems and making early data-driven design decisions saves downstream teams hours of work, reduces wastage, and decreases the risk of product delays.

Although the “A” in FEA stands for analysis, in the product development process, an FEA model is used to predict rather than analyze. It helps calculate parameters that would be too challenging, expensive, or potentially dangerous to recreate and measure in the real world with results more accurate than analytical models for complex structures.

FEA originated as a method of stress analysis in the design of aircraft. Today it’s used across various industries, from civil engineering (for analyzing things like beams, plates, and foundations) to ship-building, motor, and engine design. Rapid advances in computing speed and lower hardware costs have spread the use of FEA far and wide, leading to a proliferation in popular FEA packages.

This is what the FEA workflow looks like:

  1. It all kicks off with a complex geometry model using CAD, often simplified to remove unnecessary elements.
  2. This geometry is then discretized-broken down into smaller elements, as we mentioned earlier. Collectively, these elements are called a “finite element mesh.”
  3. Material properties, boundary conditions, and specific load cases are applied to the mesh.
  4. The computer does its magic (aka solves thousands of discrete algebraic formulations.) 
  5. Finally, the “post-processor” presents its results through numbers and visualizations.

Limitations of FEA

FEA does have some shortcomings. While it’s a powerful numerical technique for mimicking the real world, it can’t replicate reality. You can set distinct parameters like shape, boundary conditions, and loads, but the solutions obtained are only approximate. 

What’s more, FEA’s answers are totally dependent on the human operator, software, and data inputs. All of these are fallible. Humans make mistakes, the software contains bugs, and poor quality data produces poor quality results-garbage in, garbage out. All this means you can’t trust FEA’s answers blindly. 

Furthermore, experts in the field like SS Bhavikatti, in his Finite Element Analysis 4th Edition, write about the risk of becoming over-reliant on FEA, reducing complex problems to drastic assumptions. An engineer who performs calculations manually “gets the feel of the structure and… a rough idea about the expected results.” It’s better to use FEA to refine numerical results than rely on the technique entirely.

Some Important Definitions

If you’re new to FEA and/or not from an engineering background, the wealth of different terms in the field can be intimidating. Below, I give a brief overview of some of the key terms and their meanings.

Linear and Nonlinear Analysis

A linear analysis predicts the behavior of a material like a metal spring which retains a constant stiffness when subjected to a force (until it hits a predictable failure point.) In other words, the outcome is always the same and well-understood. Most CAD packages include linear FEA. 

99% of the time, however, the relationship between the force and the subsequent displacement of the material is nonlinear. The outcome is unpredictable-you don’t know how the material will respond, at least not without carrying out thousands of complicated calculations with your FEA package.

Static and Dynamic Analysis

Static analysis is relatively straightforward, and dynamic is very complex. What differentiates the two is time. What does that mean!?

If a load is applied so slowly that inertia is irrelevant, and the load doesn’t change, then static analysis is sufficient. If, however, things start happening fast, the load changes, or everything starts to vibrate, it’s a dynamic analysis situation.

Bonus definition: Modal analysis predicts how natural frequencies (eigenfrequencies and eigenmodes) affect your object. You can use modal analysis to predict vibration problems like resonance.

Mesh Convergence

Mesh convergence relates to the minimum size your elements (little blocks) need to be to ensure an accurate result. Typically, the smaller each individual element, the greater the solution, although this must be tested.

In Summary: FEA Is Everywhere

The benefits of finite element analysis applications are wide-ranging. Here are some of the benefits.

With FEA, you can:

  • Optimize and increase the efficiency of design cycles
  • Root out problems early, eliminating expensive downstream disasters
  • Maximize product performance, cost efficiency, and safety
  • Create a virtual instead of a physical prototype to reduce R&D and development costs
  • Increase productivity, profitability, and sustainability

It’s no wonder that since its inception in 1960 (when Dr. Ray Clough first coined the term “finite element”), the FEA software market has grown to over $4 billion and is expected to reach $11 billion by 2030.

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