Finite Element Analysis Explained: Design Optimization Made Simple

What Does It Mean?
“Finite Element Method” V.S. “Finite Element Analysis”

Finite Element Method (FEM) is a way to divide a complex object into many small and simple parts called elements. Each element has simple equations. Together, these equations show how the full object behaves under forces, heat, or other conditions.

Finite Element Analysis (FEA) is a computer method that helps engineers predict how a real part or structure behaves under different conditions. The FEA uses the FEM to divide a complex object into many small, simple parts called elements. These elements are connected together at nodes.
The creation of the discrete elements is called discretisation, and the collection of nodes and elements is called a mesh.
Each element has respective equations that describe how the element reacts to forces, pressure, heat, or other effects.
The computer links all the equations of the elements together, and solves them as one large system of equations.
The solution (of the system of equations) shows what happens to the whole object.

Finite element analysis helps engineers find:

• Natural frequencies and mode shapes: How the object vibrates
• Displacement: How much a part of the object moves under load
• Stress and strain: Where a part of the object might bend or break
• Temperature and heat flux: How heat flows through the object
• Flow and pressure: How fluids move inside or around the object

In this article, we will imagine that the object of analysis is a blade of a wind turbine.

Which Problems Does Finite Element Analysis Solve?
Types Of Analyses

Engineers typically use the finite element analysis to solve problems for machines in real-life.
These problems are related to different types of analysis:

Static Structural Analysis

Static structural analysis is to find stress, strain, and displacement under constant loads. To confirm that the part or structure is strong and safe.
How: Apply steady forces or pressures and solve for internal stresses and deformations.

Modal Analysis

Modal analysis is to find natural vibration frequencies and mode shapes. To avoid resonance and vibration failure.
How: Remove all loads, apply only mass and stiffness, and solve for natural frequencies.

Harmonic (Frequency Response) Analysis

Harmonic analysis is to find how a part reacts to sinusoidal or frequency-varying loads. To study vibration behavior under rotating or oscillating equipment.
How: Apply dynamic loads that change with frequency and solve for steady-state vibration response.

Transient Dynamic Analysis

Transient dynamic analysis is to find how motion, stress, and strain change with time. To understand impact, shock, or time-dependent loading effects.
How: Apply time-varying loads and solve motion equations step by step over time.

Buckling Analysis

Buckling analysis is to predict the critical load that causes sudden structural instability. To prevent failure of slender parts under compression.
How: Apply compressive load and calculate the load factor where buckling starts.

Thermal Steady-State Analysis

Thermal steady-state analysis is to find temperature distribution when heat flow is constant over time. To check if temperatures stay within safe operating limits.
How: Apply constant heat sources, convection, or radiation and solve for steady temperatures.

Thermal Transient Analysis

Thermal transient analysis is to find temperature changes over time when heat sources vary. To study cooling or heating cycles and temperature gradients.
How: Apply time-dependent heat loads and solve temperature equations at each time step.

Thermal Stress Analysis

Thermal stress analysis is to find stress caused by temperature differences or expansion. To prevent cracking or distortion from uneven heating.
How: Use temperature results as input for a structural analysis to find thermal stresses.

Contact Analysis

Contact analysis is to study how two or more parts touch, press, or slide. To predict pressure distribution, wear, or joint performance.
How: Define contact surfaces, friction, and loads, then solve for contact forces and deformation.

Fatigue Analysis

Fatigue analysis is to predict failure from repeated or cyclic loading. To estimate product life and avoid fatigue cracks.
How: Use stress history and material fatigue data to calculate life cycles before failure.

Creep Analysis

Creep analysis is to study slow, permanent deformation over long periods under constant load and high temperature. To predict long-term performance of materials in hot environments.
How: Use material creep data and apply sustained loads and temperature for long time steps.

Nonlinear Material Analysis

Nonlinear material analysis is to model materials that do not behave linearly, such as plastic or rubber. To get accurate results for large deformation or plastic flow.
How: Define nonlinear material properties and solve iteratively until stress and strain stabilize.

Fluid-Structure Interaction (FSI)

Fluid structure interaction is to study how fluids and solids affect each other. To predict performance of systems where pressure or flow changes structure shape.
How: Couple fluid and structural solvers so both influence each other during simulation.

Multiphysics Analysis

Multiphysics analaysis is to combine two or more physical effects, such as thermal, structural, fluid, or electrical. To simulate real-world systems that involve multiple energy types.
How: Link different physics solvers and exchange results between them during each step.

Steps For The Finite Element Analysis:

1. Define The Problem
& Understand The physical Properties Of the object

To define the problem, it is necessary to define the goal of the analysis.
For example, is the goal to estimate the product life cycle? In this case, a fatigue analysis is necessary.
Another example is the goal to predict cracks that result from uneven heating. In this case, a thermal stress analysis is necessary.
The defined problem is correlated with the object behavior that you want to simulate.

In addition, it is necessary to deeply understand the phyiscal properties of the object, to prepare for the finite element analysis.
These physical properties of the object of analysis can include:

• Forces, heat, pressure, or motion that act on the object.
• Weak areas, sharp corners, or high-stress zones in the object.
• If the object stays in the same shape, or if it changes shape a lot.

2. Divide The Problem Into Smaller Parts

It is necessary to divide the problem into smaller parts. The division into smaller parts helps to identify key parameters for the problem. The more accurate the key parameters, the more accurate the simulation.
A typical division of the problem can include the identification of the:

• Blade geometry
• Material properties
• Boundary conditions
• Loads & environmental factors

3. Setup The Key Parameters Of The Problem

• Density
• Young’s modulus (stiffness)
• Poisson’s ratio
• Strength limits (tension, compression, shear)
• Fatigue properties (optional for long-term analysis)

Note!
It is important to define if the material is isotropic or anisotropic:

• Isotropic materials have the same behavior in all directions. Steel and aluminum are isotropic. It is necessary to use isotropic data for basic analysis.
• Anisotropic materials have different behavior in different directions. Composites like Glass Fiber Reinforced Polymer (GFRP) are anisotropic. It is necessary to use anisotropic or composite data for the blade of a wind turbine.

In addition, the loads and other environmental factors can include, for example:

• Wind pressure along the blade
• Gravity
• Centrifugal force due to rotation
• Aerodynamic lift and drag
• Temperature (if thermal effects matter)
• Moisture or corrosion
• Extreme load cases (gusts, storms)

4. The Mesh = Discretisation Into Elements & Nodes

This step is about the generation of a mesh that divides the 3D model into many small elements, and these elements are connected together at nodes. Each element has respective equations that describe how the element reacts to forces, pressure, heat, or other effects.
The computer links all the equations of the elements together, and solves them as one large system of equations.
The solution (of the system of equations) shows what happens to the whole object. This way, it is possible to calculate stress, strain, and displacement accurately.
A good mesh gives accurate results.
A poor mesh gives wrong results, even when loads and materials are correct.

How to generate the mesh:

1. Select the correct element type for the part:
   • Solid elements suit thick parts.
   • Shell elements suit thin parts.
   • Beam elements suit long and slender structures.
     The correct element type gives the model the correct stiffness and behavior.
     For a thick-walled structure like a blade of a wind turbine, solid meshing is often recommended.
2. Set the element size according to part complexity:
   • A larger size creates fewer elements and faster solving.
   • A smaller size creates more elements and higher accuracy. Use one main size for most of the part. Apply smaller sizes in areas with high stress or complex shape.
3. Let the software generate the mesh based on these rules.
4. Do a quality check of the mesh. It is necessary to make sure that the elements have a regular shape, and that the elements do not stretch too much or collapse. The mesh must follow the geometry and show smooth transitions between large and small areas.
5. Do a refinement of the mesh. Critical areas, such as high-stress points near the root, tip, or complex geometry features, may require a finer mesh. Therefore, experiment and reduce element size in critical areas or increase size in simple areas. This can improve accuracy in stress and displacement results.
6. Apply final adjustments to the mesh, according to the experimentation and refinement of the mesh.
7. Do a mesh convergence test, to confirm that the element size is correct.

Note!
A mesh convergence test is to check if the results stay accurate when the mesh changes.
It is to note key results from the mesh, such as maximum stress. Then, reduce the element size and solve again. Compare the results. Repeat this test until the results of maximum stress change very little between meshes
When results do not change significantly, the mesh is converged and the solution can be considered reliable.

5. Run the simulation for Finite Element Analysis

7. Optimize the design

The end-goal of these simulations, calculations, and analyses is to optimize the design of a machine. To optimize the design is to improve performance, and at the same time, make sure that safety and functional reliability of the machine are up to a high standard too.

Explore some techniques to optimize the design:

1. Experiment with changes in the wall thickness to evaluate its effect on structural performance. The aim is to achieve an optimal balance, make sure that the blade of a wind turbine (for example) remains lightweight while being strong enough to withstand wind pressures without excessive deflection.
2. Try advanced optimization methods, such as topological optimization. This is to reduce material usage but also keep strong structural integrity.
3. Then, compare the performance of various design iterations, and select an optimal configuration, based on simulation data.

Conclusion

• The finite element analysis makes it possible to turn technical data into practical insights that improve real-world design.
  Through iterations and simulations, experimentation with parametric studies, and examination of the results, it is possible to make the design of a machine stronger, lighter, and safer.
• To know basic engineering principles, like how wind pushes on structures, how materials handle stress, and how shapes affect stability, is a solid foundation for accurate structural analyses.