The finite element method (FEM) is essentially very complex math used by engineers to reduce the number of prototypes and virtual experiments necessary to create a successful design. In previous posts, we discussed the advantages of the finite element method (FEM) and finite element analysis (FEA). Together, FEM and FEA are used to predict the structural behavior and integrity of a design.
Specialized finite element analysis software emerged in the 1970s. Now, it is common to find virtual testing integrated into the product development cycle. The global simulation software market size reached US$11.08 billion in 2020. It’s expected to grow 17.5% by 2028 while the specific FEA software market is anticipated to grow nearly 9% over the same period.
Key factors to support this expected market revenue growth across several industries include the increasing need to reduce manufacturing costs, as well as the need to investigate critical situations without actual risks. Simulation software for problem solving and decision making will be important at almost every stage of manufacturing, including product design, testing, and market launch, to mitigate potential challenges and boost financial returns. These are just a few of the ways that various industries utilize FEM and FEA.
Manufacturing Industry
The manufacturing industry is facing problems due to a significant increase in manufacturing costs, rapid demand fluctuations, and excessive equipment investment. Consequently, the industry is faced with the challenge of simultaneously achieving eco-friendly, high-quality, and low-cost products. To meet these demands, organizations are making an effort to improve the efficiency of the manufacturing process using FEM to predict various variables such as die alignment, material size deviation, and working temperature.
Energy Industry
Currently, rethinking energy transport is essential due to its broader applications for different energy systems. The study of heat and mass transportation has received remarkable consideration by physicists, engineers, and mathematicians. Researchers are looking at how to boost thermal transportation by mixing the nanoparticles in the base fluid mixture. Utilizing FEA, they are working to find numerical and graphical outcomes related to velocity and temperature versus various parameters. The present developments are applicable in automobile coolants, as well as the dynamics in fuel and the production of solar energy.
Rail Industry
In designing for passenger rail vehicle safety, one of the most challenging tasks for design engineers in the rail industry is predicting material durability. Numerical simulation is a convenient solution for prediction challenges, but a model’s predictions strongly depend on the availability—and accuracy—of material and assembly data. Advanced adhesive properties can provide designers with a robust data package to address modeling challenges through complex calculation methods or FEA. For multiple passenger rail interior and exterior applications, 3M has characterized three of its structural adhesive technologies to meet data requirements for two safety classes.
Commercial FEA Software
Ansys Mechanical recently became one of the first commercial finite element analysis (FEA) programs supporting AMD Instinct™ accelerators, which are the newest data center graphics processing units (GPUs). The accelerators are designed to provide exceptional performance for data centers and supercomputers to help solve the world’s most complex problems.
“Today’s large, complex engineering challenges require quick, predictively accurate simulations that scale,” said Brad McCredie, corporate vice president at AMD. The collaboration between Ansys and AMD will enable a notable speed boost for applications, which will allow researchers to run complex structural simulations in order to drive higher quality, more efficient designs for cars, planes, and a range of other products.
Discover the Finite Element Method (FEM)
Learn one of the most powerful numerical approaches available to engineers. Finite Element Method for Photonics, a five-course program, covers the fundamental principles of FEM while providing participants with insight into the method.
Connect with an IEEE Content Specialist today to learn how to get access to this program for your organization.
Interested in access for yourself? Visit the IEEE Learning Network (ILN)
Resources
3M. (17 August 2022). Designing for passenger rail vehicles safety and durability. Railway Gazette International.
Ansys. (24 August 2022). Ansys and AMD Collaborate to Speed Simulation of Large Structural Mechanical Models Up to 6x Faster. Cision PR Newswire.
Brush, Kate. (Accessed 30 August 2022). DEFINITION: finite element analysis (FEA). TechTarget.
Emergen Research. (10 August 2022). Global Simulation Software Market Is Expected to Grow Steadily At CAGR Of 17.5% In The Forecast Period Of 2021-2028. EIN Newswires.
Ho Seo, Young. (2 August 2022). Development of smart cold forging die life cycle management system based on real-time forging load monitoring. Scientific Reports.
Infinium Global Research. (July 2022). Finite Element Analysis [FEA] Software Market: Global Industry Analysis, Trends, Market Size, and Forecasts up to 2028. Research and Markets.
Sohail, M., Nazir, U., El-Zahar, E.R. et al. (5 August 2022). Galerkin finite element analysis for the augmentation in thermal transport of ternary-hybrid nanoparticles by engaging non-Fourier’s law. Scientific Reports.
The finite element analysis (FEA) is leading to major breakthroughs in nanotechnology, and having a huge impact on a number of industries spanning electronics, material science, quantum science, engineering, and biotechnology, AZO Nano reported.
Simulations based on FEA, a complex mathematical technique, is giving engineers valuable insight into the mysterious mechanical properties of polymer nanocomposites used as filler in polymer manufacturing and processing. These properties offer a revolutionary alternative to conventional polymer composites, including enhanced abrasion resistance, less shrinkage, and residual stress, as well as advanced thermal, electrical, and optical properties.
Nanomaterials are much smaller than traditional materials, and are therefore typically not as effective. As such, it is crucial for engineers to understand how the materials will react under stress in order to improve their design. While FEA is just one technique used to test these designs, its unique abilities provide significant insight into their properties.
What is FEA?
As we previously reported, FEA is based on the finite element method (FEM), a technique that can help solve highly complex math equations. A simple way to understand FEM is to look at it as separating a large problem into a series of smaller ones (“finite elements”), making the overall problem easier to see. FEA is the mathematical equations behind FEM that is applied to create a simulation. The simulation breaks down the entire model into smaller elements within a mesh, which engineers use to test how the different elements of a design interact and perform under simulated stressors.
There are many benefits of using FEA. For one, its insight into how the various elements of a design are interacting in minute detail provide enhanced accuracy of structural analysis. Furthermore, FEA allows engineers to create virtual simulations thereby reducing the need for physical prototypes and testing in order to save time and money.
How Are Engineers Using FEA for Advancing Nanotechnology?
Using FEA, researchers have discovered that high interfacial stress can cause the nanofiber or matrix in the material to come apart. They were able to control the properties which improve the strength of the interface to generate the best stress transfer. They discovered that the accumulation of stress concentrations at the interface between the fiber and the matrix can reveal the effective matrix-to-nanofiber stress transfer. Additionally, engineers can use FEA to simulate the composition of nanocomposites and nanotubes in the polymer, which would strengthen their mechanical properties by organizing thousands of nanotubes in a specific pattern.
What Industries Are Benefiting From This Research?
The aerospace sector is using FEA to model and test the effectiveness of polymer nanocomposites-based structures. FEA is also used by the manufacturing sector to simulate the necessary properties of polymer nanocomposites for use in packaging and coating applications.
Engineers are also using FEA to make breakthroughs in the field of photonics. Examples include using FEA to analyze four-wave mixing of topological edge plasmons in graphene metasurfaces; to demonstrate a feasible way to control light on integrated photonics and free-space metasurfaces; and to develop advancements in surface-emitting semiconductor lasers and optical lenses. Learn more about how photonics researchers are using FEA to advance their field.
Problem-Solving Applications with Photonic Devices
Providing a comprehensive and up-to-date account of FEM in photonics devices, with an emphasis on practical, problem-solving applications and real-world examples, Finite Element Method for Photonics is a five course-program from IEEE. Created by Dr. Agrawal, learners will gain an understanding of how mathematical concepts translate to computer code finite element-based methods after completing this program.
Connect with an IEEE Content Specialist today to learn how to get access in order to train your organization.
Interested in the course program for yourself? Visit the IEEE Learning Network (ILN).
Resources
Ahsan, Muhammad Adeel (27 April 2022). Finite Element Analysis of Polymer Nanocomposites. AZO Nano.
Researchers from Tokyo University of Science have developed a new design method that could lead to lighter, faster, and cleaner vehicles and airplanes. Their technique, published in Composite Structures, simultaneously optimizes fiber thickness and orientation. As a result, it reduces the weight of reinforced plastic parts commonly used in aerospace, civil engineering, and sports equipment.
Traditionally, efforts have mostly focused on enhancing the strength of carbon fiber composites. However, the Tokyo researchers’ new design method optimizes both fiber thickness and orientation. Typically, carbon fibers are combined with other materials to make a composite, such as carbon fiber reinforced plastic (CFRP), which is popular for its strength, rigidity, and high strength-to-weight ratio. Some studies have examined how to improve CFRPs, particularly through a technique called “fiber-steered design,” which optimizes fiber orientation to enhance strength. The fiber-steered design approach, however, had a major flaw.
“Fiber-steered design only optimizes orientation and keeps the thickness of the fibers fixed, preventing full utilization of the mechanical properties of CFRP,” research team member Dr. Ryosuke Matsuzaki told Canadian Plastics. “A weight reduction approach, which allows optimization of fiber thickness as well, has been rarely considered.”
“Simultaneous Optimization Technique” Reduces CFRP Weight Without Affecting Strength
Faced with this dilemma, the researchers proposed a new design technique for simultaneously optimizing orientation and thickness depending on the composite structure’s location, which reduced the CFRP’s weight without affecting strength. According to their research, the method includes three phases.
- The Preparatory Phase:
During this phase, the researchers performed an analysis using the finite element method (FEM). As we discussed in a previous post, FEM is a numerical solution that breaks down a much larger, complex problem into a series of smaller ones (“finite elements”) in order to make the overall problem easier to examine. This equation is then used to create a digital simulation known as the finite element analysis, which gives engineers a more detailed look into the design and how its various elements work together. The team used the simulation “to determine the number of layers, enabling a qualitative weight evaluation by a linear lamination model and a fiber-steered design with a thickness variation model.” - The Iterative Phase:
The team implemented the iterative process to “to determine the fiber orientation by the principal stress direction and iteratively calculate the thickness using ‘maximum stress theory.’” - The Modification Phase:
During this step, the researchers made “modifications accounting for manufacturability by first creating a reference ‘base fiber bundle’ in a region requiring strength improvement and then determining the final orientation and thickness by arranging the fiber bundles such that they spread on both sides of the reference bundle.”
This simultaneous optimization technique led to a weight reduction of more than five percent and allowed for higher load transfer efficiency than what fiber orientation achieves by itself. In the future, the method could reduce the weight of CFRP parts that support greener transportation systems.
“Our design method goes beyond the conventional wisdom of composite design, making for lighter aircraft and automobiles, which can contribute to energy conservation and reduction of CO2 emissions,” Dr. Matsuzaki told Canadian Plastics.
FEM analysis is becoming an increasingly popular research tool, including in the field of photonics, where the method has contributed to a number of recent breakthroughs. Check out some of the latest innovations in optics research supported by this simulation tool.
Finite Element Method (FEM) for Photonics
Learn how FEM can be used to model and simulate photonic components/devices and analyze how they will behave in response to various outside influences. The Finite Element Method for Photonics course program provides a comprehensive and up-to-date account of FEM in photonics devices, with an emphasis on practical, problem-solving applications and real-world examples. Engineers will gain an understanding of how mathematical concepts translate to computer code finite element-based methods after completing this program.
Connect with an IEEE Content Specialist today to learn how to get access to this program for your organization.
Interested in the course for yourself? Visit the IEEE Learning Network (ILN).
Resources
Tokyo University of Science. (24 May 2021). New optimization approach helps design lighter carbon fiber composite materials. ScienceDaily.
Tokyo University of Science. (2 June 2021). Tokyo researchers hit on new design method to reduce weight in reinforced plastics. Canadian Plastics.
The optics and photonics fields are creating groundbreaking applications for astronomy, telecommunications, sensing, chemistry, biomedical research & development.
Recently, researchers from Pennsylvania State University demonstrated how metasurfaces with unparalleled controllability of light may be able to transform traditional optics. To do so, they used a simulation that applied the finite element method (FEM).
As discussed in a previous post, FEM is a numerical solution for a complex problem, which breaks down a much larger problem into a series of smaller ones (“finite elements”), making the overall problem easier to pick apart. This equation is then used to create a simulation (known as the finite element analysis), which gives engineers a more detailed analysis into the design and how its various elements work together.
How Engineers Used FEM to Demonstrate the Potential of Metasurfaces
“Metasurfaces” are thin, two-dimensional metamaterial layers that permit or prevent the propagation of electromagnetic waves in desired directions. They are thought to have enormous potential to transform traditional optics technology.
However, metasurfaces do pose some problems. For instance, metasurfaces depend on the excitation of external light. Because of this, it’s challenging to integrate the layers completely onto a single chip. Conversely, while integrated photonics allows optical components to be packed compactly onto a chip, there’s not enough space to control light.
The Pennsylvania State researchers found a solution: they dressed metasurfaces onto waveguides. These structures can guide waves—including electromagnetic waves. By doing this, they molded guided waves into the free-space modes they desired. The process allowed them to create complex free-space functions, like out-of-plane beam deflection and focusing.
Using FEM simulations, the researchers demonstrated a feasible way to control light on integrated photonics and free-space metasurfaces. The study may represent a path forward for scientists to be able to make multifunctional photonic integrated devices with the ability to easily access free space, allowing for a range of advancements in optical communications.
“We have experimentally demonstrated off-chip beam deflection and focusing using the guided wave driven metasurfaces on silicon waveguides. In addition, two-dimensional (2D) manipulation of free-space light can be realized by placing a 2D array of meta-atoms on a slab waveguide. This technology can enable a wide spectrum of applications ranging from optical communications to LiDAR, as well as miniaturized display technology for virtual reality and augmented reality devices,” the researchers wrote in Science Advances.
This study is just one example of how researchers are using FEM to make breakthroughs in optics and photonics. Another team of researchers recently used FEM to demonstrate a potential new way to develop innovative applications in quantum communications and information processing.
Finite Element Method (FEM) for Photonics
This course program from IEEE Educational Activities, Finite Element Method for Photonics, provides a comprehensive and up-to-date account of FEM in photonics devices, with an emphasis on practical, problem-solving applications and real-world examples. Engineers will come away from this program with an understanding of how mathematical concepts translate to computer code finite element-based methods.
Contact an IEEE Content Specialist today to learn more about getting access to these courses for your organization.
Interested in the course for yourself? Visit the IEEE Learning Network.
Resources
Chen, Xi, Ding, Yimin, Duan, Yao, Guo, Xuexue, Ni, Xingjie (17 July 2020). Molding free-space light with guided wave–driven metasurfaces. ScienceAdvances.
The Benefits of Finite Element Analysis in Manufacturing. Manor Tool.
Agrawal, Arti , Rahman, B. M. Azizur. (2013). Finite Element Modeling Methods for Photonics. Artech House.
Photonics is the science of producing, manipulating, and discovering light waves and photons (light particles). The field covers a number of technologies like lasers and fiber-optics. In particular, the finite element method (FEM) can be used to create a range of photonics applications. For example, researchers apply these in astronomy, telecommunications, sensing, chemistry, biomedical R&D, and more.
How is the Finite Element Method Used in Photonics?
At its core, FEM is a numerical solution for a complex problem, which breaks down a much larger problem into a series of smaller ones (“finite elements”). This makes the overall problem easier to decipher. Engineers then use this equation to create a simulation, or what’s known as the finite element analysis, to test how different elements of a design react. They evaluate reactions to different simulated stressors. As a result, FEM is a popular technique among engineers to effectively simulate photonics devices and components. It helps them understand how they will react and behave under external environmental factors. It has been fueling breakthroughs in photonics.
How FEM is Helping Photonics Researchers Make Discoveries
Recently, researchers used FEM to analyze topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface. This surface was made up of intermittent arrangements of nanoholes in a graphene sheet. They demonstrated a broad topological energy gap at terahertz frequencies during the breaking of time reversal symmetry by a static magnetic field. The scientists revealed that they were able to achieve a net gain of FWM synergy of plasmonic edge states within the topological bandgap. The pump power was less than 10 nW. Additionally, they demonstrated that the adequate nonlinear edge-waveguide coefficient is over 10 orders of magnitude greater. This is compared to that of highly nonlinear silicon photonic nanowires that are typically employed.
“These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale,” the researchers write in Science Advances. They believe these applications are promising for quantum communications and information processing.
Surface-emitting semiconductor lasers can be used for sensing, data communications, facial recognition, and augmented reality glasses. In a recently published report, researchers from the U.S., Korea, and Canada, documented the first-ever all-epitaxial, distributed Bragg reflector (DBR)-free, electrically injected surface-emitting green laser. Specifically, the team used a 2D-FEM simulation to test the design.
“The results provided strong evidence on achieving coherent lasing oscillation in InGaN nanocrystal arrays,” writes Thamarasee Jeewandara in Phys.org. “The scientists measured the electroluminescence spectra to demonstrate remarkably stable and directional polarized emission. This was compared to conventional photonic crystal laser devices.”
Other Uses of FEM
Beyond lasers, scientists also apply FEM to examine how topological protection applies to photonics. This could create new ways of directing and controlling quantum information. For example, one group of researchers recently demonstrated that spin-orbit coupling can produce helical edge states. Their experiment demonstrated one-way propagation that topologically safeguards against backscattering.
The scientists witnessed the electronic materials’ photonic analog topological states undergoing the quantum spin Hall effect. They observed this between a pair of silicon photonic crystals consisting of different topological order. The researchers used the associated innate far-field radiation to label their properties, such as linear dispersion and low loss.
“We find that the edge state pseudospin is encoded in unique circular far-field polarization and linked to unidirectional propagation,” the scientists write. “This reveals a signature of the underlying photonic spin-orbit coupling. We use this connection to selectively excite different edge states with polarized light. This allows direct visualization of their routing along sharp chiral waveguide junctions.”
Finite Element Method (FEM) for Photonics
The new course program from IEEE Educational Activities, Finite Element Method for Photonics, provides a comprehensive and up-to-date account of FEM in photonics devices. It emphasizes practical, problem-solving applications and real-world examples. Engineers will come away from this program with an understanding of how mathematical concepts translate to computer code finite element-based methods.
To put these concepts into practice, connect with an IEEE Content Specialist today and learn how to get access to this program for your organization.
Interested in the course for yourself? Visit the IEEE Learning Network (ILN).
Resources
Wei You, Jian, Lan, Zhihao, and Panoiu C, Nicolae. (27 March 2020). Four-wave mixing of topological edge plasmons in graphene metasurfaces. Science Advances.
Parappurath, Nikhil, Alpeggiani, Filippo, Kuipers, L., and Verhagen, Ewold. (6 March 2020). Direct observation of topological edge states in silicon photonic crystals: Spin, dispersion, and chiral routing. Science Advances.
Jeewandara, Thamarasee. (16 January 2020). An electrically pumped surface-emitting semiconductor green laser. PHYS.ORG.
Agrawal, Arti , Rahman, B. M. Azizur. (2013). Finite Element Modeling Methods for Photonics. Artech House.
The finite element method (FEM) and finite element analysis (FEA) work together to give engineers insight into the structural behavior of designs. This combined approach helps them locate weak points and strengthen performance.
FEM
Engineers developed FEM in the mid‑1950s to provide numerical solutions for complex problems. In practice, FEM allows for some degree of error, making it useful when equations are too complicated to solve directly. Put simply, FEM breaks a large problem into smaller ones (“finite elements”), which makes the overall challenge easier to investigate. Engineers rely on FEM when they need to design adaptable solutions. Although practical, FEM does not always deliver perfect results for every application.
FEA
Engineers apply the mathematical equations behind FEM to create a simulation, known as a finite element analysis (FEA). Through these simulations, they can analyze how a product or design reacts under stress in real‑world conditions. The simulation divides the model into smaller elements within a mesh. By doing so, engineers test how different parts of a design interact and perform under simulated stressors.
In other words, FEA provides a virtual model that lets engineers experiment with structural designs using software. Together, FEA and FEM predict the structural behavior and integrity of a design.
Trevor English explains in Interesting Engineering:
Complex mathematics is required in order to understand the physical phenomena that occur all around us. These include things like fluid dynamics, wave propagation, and thermal analysis…Yet, in complex situations where multiple highly variable equations are needed, Finite Element Analysis is the leading mathematical technique.”
Trevor English, Interesting Engineering
Benefits of FEM and FEA
Improved accuracy and enhanced design: FEM and FEA allow for enhanced accuracy of structural analysis. They give insight into how the various elements of a design interact in minute detail. Engineers can investigate both the interior and exterior of a design.
Faster and inexpensive testing: Because FEM and FEA allow engineers to create virtual simulations, they reduce the need for physical prototypes and testing. This saves time and reduces costs.
Applications of FEM and FEA
Traditionally, FEM was used to test designs within aerospace and civil engineering. However, it is now expanding to other disciplines. These include biomechanics, thermomechanical, fluid-structure interaction, biomedical engineering, ferroelectric, thermo-chemo-mechanical problems, piezoelectric, and electromagnetics.
The mathematical principles behind FEM can also be applied to other areas. These include computational fluid dynamics (CFD) and the thermal dynamics of a structure.
“For example, if you know the temperature at one point in an object, how would you determine the exact temperature at other points of the object, dependent upon time?” writes Trevor English in Interesting Engineering. “Utilizing FEA, an approximation can be made for these points using different modes of accuracy. There’s a square approximation, a polynomial approximation, and a discrete approximation. Each of these techniques increases in accuracy and complexity.”
Learn the Finite Element Method (FEM)
The new course program from IEEE Educational Activities, Finite Element Method for Photonics, provides a comprehensive and up-to-date account of FEM in photonics devices. It emphasizes practical, problem-solving applications and real-world examples. Engineers will gain an understanding of how mathematical concepts translate to computer code finite element-based methods.
Connect with an IEEE Content Specialist today to learn how to get access to this program for your organization.
Interested in the course for yourself? Visit the IEEE Learning Network (ILN).
Resources
Gigantic, Michael. (10 September 2020). What Is Finite Element Analysis? Learning Hub.
English, Trevor. (7 November 2019). What Is Finite Element Analysis and How Does It Work? Interesting Engineering.
Harish, Ajay. (21 Mar 2019). Finite Element Method – FEM and FEA Explained. SimScale.
The Benefits of Finite Element Analysis in Manufacturing. Manor Tool.