What is finite element analysis (FEA)?
Finite element analysis (FEA) is the process of simulating the behavior of an object or assemblage of objects when it's exposed to specified physical conditions, which can be stable or varying. FEA attempts to predict how the object might behave under those conditions and what that might mean to the underlying design.
Finite element analysis incorporates mathematical calculations and models into the analysis process to create computer simulations that predict the object's behavior. Engineers use FEA to find vulnerabilities in their designs when those designs are subjected to simulated forces such as temperature variations, extreme heat, changes in pressure, seismic activity, wind speed or other variables.
Finite element analysis is based on the finite element method (FEM), a numerical technique that breaks the object's structure into tiny units called elements and then reconnects the elements at points called nodes. From there, the FEM applies partial differential equations (PDEs) to each element, which are then used to generate comprehensive predictions of the object's behavior.
Finite element analysis emerged as a way for computers to solve both linear and nonlinear PDEs. However, FEA offers only an approximate solution to predicting an object's behavior under specified conditions. It is essentially a mathematical approach to predicting real-world results, which is not the same as testing physical prototypes.
Even so, FEA can significantly reduce the number of physical prototypes that designers need to create during product development. It can also reduce the number of experiments they must perform and optimize components during the design phase.
Finite element analysis software emerged in the 1970s with programs such as Abaqus, Adina and Ansys. Virtual testing and design optimization are now commonly integrated into the product development cycle to improve quality and reduce the time it takes to enter the market.
How finite element analysis works
The FEA process starts by creating a digital model of the object to be analyzed. The model is often created in a computer-aided design (CAD) program and then imported into an FEA application, which breaks it down into elements. That said, FEA capabilities are sometimes integrated into CAD platforms or vice versa.
Depending on the object, the elements can number from thousands into millions. Each element is a simple geometric shape such as a square or triangle. Together the elements are referred to as the mesh, which forms the object's structure. The FEA software performs PDE calculations on each element in the mesh. The results of the calculations are then combined to predict the structure's behavior under the specified physical conditions.
The FEA process itself, after the initial model has been created, is commonly broken down into the following three steps:
- Preprocess. The designer selects the element type and analysis type, such as modal analysis or structural static analysis. The designer also defines the material properties as well as the element and node structure and then applies the boundary conditions and loads.
- Process. During this step, the individual element calculations are computed generating results, which are presented to the designer.
- Postprocess. The designer reviews the generated results, noting factors such as stress, strain, displacement, temperature, time history and natural frequency.
Finite element analysis requires well-defined boundary conditions to ensure accurate predictions. Boundary conditions are constraints placed on FEA calculations to reflect real-world conditions, such as forces and pressures.
Finite element analysis is also based on three governing equations:
- Equilibrium equations. Determines when the opposing forces or influences are balanced.
- Strain-displacement relations. Measures the deformation that the design experiences under an external impact.
- Constitutive equations. Determines the relations between two physical quantities, specific to the given substance, which predicts the material's response to external stimuli.
Types of FEA tests
Various types of tests are used during FEA. The following tests are some of the more common ones:
- Structural static analysis. The test analyzes a scaled model based on the object's proportions. It assumes that any structure that is sound on a small scale will be able to handle the same interactions with the full-scale structure and produce the same results.
- Thermal engineering analysis. The test explores variations in temperature and how it affects the design structure.
- Modal analysis. The test determines how external vibrations can disrupt the product's structure. It also enables designers to adjust for vibrations throughout the design stage, thus creating a stronger final product.
- Engineering seismic calculations. This test helps designers understand the product's performance when dealing with various ground frequencies and vibrations, ensuring a sturdy location for the final structure.
Common finite element analysis use cases
In recent years, FEA has grown in scope, capability and use cases. It is commonly employed in aerospace, automotive and civil engineering projects as well as biomechanics. It is particularly useful for designing machinery and analyzing the parts for fatigue and other issues.
Addition use cases for FEA include the following:
- Certifying crane load capacities.
- Building airport bridges.
- Determining brake or rotor lifetime certifications.
- Improving the performance of new and existing products.
- Ensuring compliance with legal and contractual requirements.
- Defining a product's useful life and establishing its servicing schedules.
Advantages of FEA
Finite element analysis provides the safe simulation of potentially dangerous or destructive load conditions and failure modes, enabling engineers to discover a system's physical response in any conditions without putting themselves at risk. FEA also offers other benefits:
- Improved design. Developers can observe how stresses within one element will affect the materials in another connected element.
- Earlier testing in the development process. Virtual prototyping allows designers to model various designs and materials in a matter of hours rather than the days or weeks it takes to build physical prototypes.
- Increased productivity and revenue. Designers can produce higher quality products in a shorter design cycle while also using fewer materials.
- Enhanced insight into critical design parameters. Designers can model both the design's interior and exterior. They can determine how critical factors affect the structure as well as why and where failures might occur.
- Optimized model usage. One common model can be used to test several failure modes or physical events.
- Access to existing experimental results. Information can be pulled from the parametric analyses of already validated models and applied to the new model.
- Testing variety. Ability to test a variety of real-world conditions on the design, which can improve product safety.
- Optimize alternative designs. Ability to evaluate and optimize alternative designs and materials while being able to analyze different basic solutions quickly.
Additional FEA advantages include more comprehensive analysis of a design's physical stress, fast calculation times, relatively low investment costs, and lower design and manufacturing costs.
Disadvantages of finite element analysis
Despite FEA's advantages, there are several important challenges that designers must consider:
- The finite element method simplifies an object's structure and uses basic integration techniques, which can lead to inaccuracies in the predictions.
- The limited number of digits available in computers can potentially lead to computational errors.
- User error, such as selecting the wrong element type or providing inconsistent units of measurement, can result in skewed or inaccurate predictions.
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