## What is Finite Element Analysis (FEA)?

Finite Element Analysis (FEA) is a computational method used to solve complex problems in engineering and physics. It is one of the most commonly used numerical analysis methods today.

FEA breaks down a large system into smaller pieces called "finite elements". These elements are represented by mathematical equations that approximate the behavior of the overall system. Powerful computers are then used to repeatedly solve these equations to predict how the system will react under various conditions.

The idea of dividing a domain into smaller elements dates back over a century. But the modern formulation of FEA was developed in the 1950s and 1960s, spurred by advances in computer technology and aerospace applications. Today, FEA is widely used across virtually every engineering field, from structural mechanics to fluid dynamics.

At its core, FEA works by creating a mesh of finite elements connected at nodes. Each element is defined by shape functions and degrees of freedom. Material properties are assigned to the elements. Equilibrium equations are formulated for each element. These local element equations are assembled into global system equations that represent the full problem. Solving these equations gives results like stress distributions and deformations.

By enabling detailed simulation, FEA allows engineers to virtually test products under real-world conditions, optimizing designs without costly physical prototypes. This powerful analysis method will continue playing a key role in engineering innovation.

## The Finite Element Method Explained

The finite element method (FEM) is the numerical method behind finite element analysis. It provides a systematic way to convert the complex partial differential equations that govern physics and engineering problems into a system of algebraic equations that can be solved on a computer.

The key steps in the finite element method are:

### Discretization into Elements

The first step is to discretize the geometry of the problem into small interconnected subdomains called finite elements. This is done by creating a mesh of the geometry. The mesh contains nodes at the corners of the elements and along the boundaries.

The field variables (such as displacement, temperature etc) are approximated by simple functions within each finite element. The complex geometry and field variables are thereby reduced to a discrete model of simple geometric elements defined by nodes and elements.

### Derivation of Element Equations

The governing equations of the problem are applied to each element to derive the element equations. This yields a set of equations describing the behavior of each element in response to forces or other inputs.

The element equations relate the field variables at the nodes of the element to the material properties and loading conditions. The physics of the problem is captured in these equations.

### Assembly into System of Equations

The element equations are then assembled into a global system of equations by imposing continuity conditions between adjacent elements. This ensures compatibility and equilibrium at the nodes shared by adjoining elements.

The result is a system of simultaneous algebraic equations with known and unknown terms. The unknowns are the field variables such as displacements at the nodes.

### Solving the Finite Element Equations

The global finite element equations can be solved to obtain the unknown field variables at the nodes using numerical methods such as Gaussian elimination. The nodal values provide an approximate solution for the entire physical domain analyzed.

This completes the finite element analysis once the results are processed and interpreted. The finite element method thereby elegantly transforms physics-based field problems into discrete algebraic equations amenable to computer solutions.

## Types of FEA

Finite element analysis can be categorized into several types based on the type of analysis required. The three main ways to categorize FEA are:

### Static vs Dynamic FEA

Static FEA calculates the effects of steady loading conditions on a structure, while ignoring inertia and damping effects. This assumes the loads and the structure's response are constant over time. Common applications include stress analysis and thermal analysis.

Dynamic FEA analyzes structural response under dynamic loading that can vary with time. Inertia and damping effects are considered. Used to study vibration, impact response, seismic analysis, blast response, and more. Requires defining loads that are functions of time.

### Linear vs Nonlinear FEA

Linear FEA uses linear elastic material models and equations to simulate the structural response. The results scale proportionally with load increases. Simpler and less computationally demanding.

Nonlinear FEA accounts for nonlinearities like plasticity, large deformations, contact surfaces, nonlinear material models, etc. More complex but can capture real material and structural behavior more accurately.

### Steady-State vs Transient FEA

Steady-state FEA calculates the system response once it reaches steady equilibrium. Used for problems where transient response is not required. More computationally efficient.

Transient FEA provides the time-dependent response from the initial state to the steady-state. Important for dynamic problems and complex nonlinear analyses. Requires more computation time.

## The FEA Process Step-by-Step

Finite element analysis involves three major steps:

### Preprocessing

Preprocessing involves creating the model and preparing it for analysis. This includes:

**Defining the geometry of the model and creating the mesh**- The geometry is divided into small elements connected at nodes. The mesh defines the resolution and accuracy of the analysis.**Applying material properties**- Materials like steel, aluminum, rubber etc. have unique properties. These need to be assigned to the elements.**Applying loads and boundary conditions**- The forces, pressures, displacements etc. acting on the model are applied as loads. The constraints are applied as boundary conditions.**Defining analysis settings**- Type of analysis, solver settings, convergence criteria etc. are defined.

### Analysis Solving

This step involves running the simulation and solving the mathematical model created during preprocessing. Complex simulations utilize powerful solvers running on high performance computers. The governing equations are solved iteratively.

### Postprocessing and Visualization

The raw analysis results are processed for understanding and visualization. Tools are used to view stresses, deformations, vector fields etc. The results are interpreted to gain engineering insight. Optimization and design changes may be carried out if needed.

## FEA Software Packages

Finite element analysis requires specialized software tools to model and solve complex simulations. There are several leading FEA software packages used in various industries and applications:

### ANSYS

ANSYS is one of the most widely used general-purpose FEA programs. It offers advanced simulation capabilities for structural, fluid, and multi-physics modeling. ANSYS is commonly used in the automotive, aerospace, electronics, and biomedical sectors. Key features include nonlinear analyses, fatigue tools, and optimization.

### ABAQUS

ABAQUS FEA software provides solutions for both routine and sophisticated engineering problems. It excels at simulating nonlinear and dynamic events. ABAQUS is popular in the automotive and aerospace industries. Key capabilities include nonlinear FEA, composite materials modeling, and co-simulation.

### Nastran

Nastran was developed by NASA and is a premier FEA solver for structural analysis. It is extensively used in the aerospace, automotive, and maritime industries. Nastran is known for its wide range of element types, material models, and failure analysis tools.

### Marc

Marc focuses on nonlinear, dynamic FEA applications. It is widely used for advanced modeling of rubbers, plastics, composites and structures undergoing large deformations. Marc has strengths in impact, penetration, blast, and crash simulations across the automotive, aerospace and defense sectors.

### Altair Hyper Works

Hyper Works is a suite of CAE software products for modeling, visualization and optimization. Its popular solvers include HyperMesh, OptiStruct, Radioss and AcuSolve. HyperWorks excels at high-performance computing for large, complex FEA simulations. It is used extensively in the automotive and aerospace industries.

This range of leading FEA software provides CAD engineers with advanced tools to conduct detailed analysis and optimize product designs. Selecting the right FEA application depends on analysis type, industry, budget and other factors.

## Benefits and Applications of FEA

Finite Element Analysis (FEA) provides significant benefits for engineering design and simulation across many industries:

**Early simulation and prototyping**- With FEA software, products can be simulated and tested virtually. This allows engineers to analyze designs digitally, identify and fix issues early in the design process, and reduce reliance on physical prototypes.**Insight into product weaknesses**- FEA reveals information about how a product will react under real-world conditions. It shows where designs are likely to fail due to stress, heat, vibration and other factors. Engineers use these insights to improve product durability.**Optimization capabilities**- FEA enables engineers to simulate many design variations and find the optimal design parameters. This allows efficient optimization of a part's shape, weight, strength, temperature resistance and other qualities.**Industries using FEA**- Many industries rely on FEA for product design and testing including aerospace, automotive, electronics, industrial machinery, biomedical, and more. Specific applications include modeling car crash scenarios, turbine blade design, microchip packaging, and stent durability.

By leveraging FEA early in the design process, engineers can develop better products faster, with fewer physical prototypes and less time spent on costly redesigns. This powerful simulation technology delivers major competitive advantages across many technology sectors.

## FEA Analysis Examples

Finite element analysis is widely used across many engineering disciplines and industries to simulate different types of physics. Here are some of the most common examples of problems that can be solved using FEA:

### Stress Analysis

FEA stress analysis calculates the stresses and deformations in a structure under load. This is useful for determining if a product will fail under expected use conditions. Stress analysis with FEA can optimize component design to be as light and strong as possible.

Stress analysis can calculate stresses caused by:

Forces (tension, compression, shear)

Pressure

Thermal loading

Centrifugal forces

Contact between components

FEA stress analysis is commonly used for:

Mechanical parts and assemblies

Civil engineering structures like bridges

Pressure vessels and piping systems

### Vibration Analysis

Vibration analysis calculates the natural frequencies and mode shapes of structures. This type of FEA simulation can determine if components will resonate or become unstable when operating at certain speeds. Vibration analysis is important for:

Turbines, engines, motors

Automotive components

Consumer products like cell phones

Architectural structures susceptible to earthquakes

FEA vibration analysis can help engineers alter the design to avoid resonance and component fatigue failures.

### Thermal Analysis

Thermal FEA analysis calculates temperatures, thermal gradients, and heat transfer in solids and fluids. This allows evaluation of steady-state and transient heat flow.

Thermal analysis is used for:

Heat exchangers, furnaces, boilers

Electronic components and PCBs

Aerospace components

Automotive engines and braking systems

Thermal FEA identifies hot spots so the design can be optimized for sufficient cooling and temperature control.

### Fluid Flow Analysis

Computational fluid dynamics (CFD) analysis with FEA evaluates fluid flow behaviors and parameters. This can simulate:

Internal and external aerodynamics of vehicles

HVAC ductwork

Chemical processing equipment

Hydraulics and fluid control systems

Weather and environmental airflow patterns

CFD analysis provides velocity, pressure, and flow visualizations to help optimize fluid system design.

## Accuracy and Validation of FEA

FEA is an approximation technique, so its accuracy depends on several factors:

**Mesh density**- Using smaller elements increases accuracy but also increases compute time. Proper meshing requires balancing accuracy and speed.**Element type**- Different element shapes have different approximations. Tetrahedral elements are faster but less accurate than hexahedral.**Material properties**- Accurate material data is required. Simplified isotropic properties can reduce accuracy.**Boundary conditions**- Accurately representing constraints and loads affects solution accuracy.**Convergence**- Solutions should converge as the mesh is refined. Lack of convergence indicates issues.

To validate FEA models, analysts use:

**Benchmark problems**- Simple problems with known solutions to compare against FEA results.**Hand calculations**- Manual calculations for simplified problems to verify FEA approach.**Experiments**- Physical prototypes and tests to validate FEA predictions.**Mesh convergence**- Refining the mesh and checking if solution stabilizes.**Energy balance**- Comparing energy added to model vs energy in solution.

Proper validation builds confidence in the FEA and allows it to be reliably used for design. Ongoing verification is key for accurate simulations.

## Limitations of FEA

All engineering simulation methods have limitations and Finite Element Analysis is no exception. While FEA can provide valuable insights, engineers should be aware of its limitations.

### Simplified Physics

FEA relies on mathematical equations and numerical techniques to represent real physical behavior. Certain aspects of physics may be simplified or approximated in the FEA model. This can lead to less accuracy in some cases. The analyst must understand the key physics and select appropriate elements, material models, boundary conditions, and other parameters.

### Mesh Dependency

The fineness of the mesh can impact the accuracy of FEA solutions. A very coarse mesh may not adequately capture the physics while an extremely fine mesh requires more computing resources. Performing mesh refinement studies is important to find the optimal mesh density.

### Garbage In, Garbage Out

The old computing adage "garbage in, garbage out" applies to FEA. If the material properties, boundary conditions, or other inputs are inaccurate, the FEA results will also be inaccurate or meaningless. Validating models with physical tests is important.

### Computational Expense

While computing power has improved tremendously, FEA of complex large-scale models can still require significant computational resources. Simplifications may be required to make the solutions tractable. Cloud computing and high performance computing clusters can help mitigate this limitation.

## The Future of Finite Element Analysis

The use of finite element analysis continues to grow as the technique becomes easier to use and more powerful. FEA is being adopted across many industries to optimize designs, reduce physical prototyping costs, and gain insights earlier in the design cycle.

Some key trends in FEA include:

**Growth of FEA usage**- More companies are utilizing FEA, even small and medium businesses. Improved interfaces and workflows are making FEA more accessible.**Cloud computing and FEA**- Running simulations in the cloud makes FEA available without large computing investments. Scalable computing resources improve turnaround times.**Emerging applications**- New areas like multi physics, topology optimization, biomechanics, and electromagnetics will drive more use of FEA.**Developments in software capabilities**- FEA software is rapidly improving. Features like automated meshing, process automation, and design optimization integrate FEA deeper into the design workflow.

As technology progresses, FEA will become even more versatile, automated, and realistic. It enables engineers to solve increasingly complex problems through detailed simulation and modeling capabilities. The future is bright for this simulation method that empowers better product design.

## Comments