The finite element method (FEM) is an established numerical method. Engineers have long used it to optimise components in the design phase, reduce the number of physical experiments and prototypes and develop better products, faster.
But this bread and butter method is starting to feel more like a club sandwich, as new industries and innovations push the FEM to understand and quantify an increasing range of physical phenomena.
The FEM was once primarily used in structural analysis within the aerospace, automotive and civil engineering industries – and later spread to consumer goods and manufacturing. But, nowadays, it can be applied to a much wider range of physics domains, including fluids, electromagnetics, multi-body dynamics and systems.
Consequently, the development of the FEM is driven more by usage patterns than specific industries, according to Oliver Rübenkönig, a consultant in the algorithms R&D department at Wolfram Research, who said: ‘The methods (such as the FEM) are not important. Ultimately, our customers would like to find solutions to their partial differential equations, and the method chosen for that is secondary.’
However, while specific industries are not a driver for FEM usage per se, the increasing range of physics domains has opened the floodgates, as Guna Krishna, vice president of product development at Altair, explained: ‘ Today, the FEM is used in many industries such as robotics to design motors, in computers to design chips and circuit boards, in biomedical applications to design heart valves, tooth implants, stents, in self-driving cars to locate the sensors, in manufacturing to reduce the number of defects, and improving the additive manufacturing process.’
Both the advancing additive and electronic industries are embracing the FEM. Bjorn Sjodin, VP of product management at COMSOL, said: ‘Additive manufacturing is a strong trend and we have plenty of users in this area. In many cases it goes hand in hand with topology optimisation and other classes of geometry optimisation, such as generative design and genetic algorithms.’ He added: ‘There is also a big interest for simulations within electric motors, batteries, and fuel cells; within the IoT, where the Internet of Things has a wide definition but we are certainly seeing users in this area; and within 5G, where the development of the next generation wireless technology is in many cases driven by advances in simulation technology.’
The traditional aerospace and automotive industries are also continuing to innovate in the FEM space, as Stuart Sampson, vice president of HyperWorks enterprise implementations at Altair, explained: ‘Composites traditionally have been the focus of aerospace and F1, now you see composites much more in mainstream automotive, see as an example the BMW i3 with its carbon fibre composite passenger cell. Modular architecture in automotive is now being applied to other non-automotive industries.’
Krishna added: ‘In the automotive industry, emission standards are shifting emphasis to low emission vehicles (such as electric and hydrogen fuel engines). Longer warranties and more passenger comfort is demanding increased analysis with multiple physics included in the analysis process. Fuel efficiency in aerospace continues to challenge the FE solutions to create efficient designs.’
Sampson added: ‘The large transportation industry – including automotive and off-highway vehicles – is also driving dramatic changes in the product development process. E-Mobility and ADAS (advanced driver assistance systems) are making connectivity and communication paramount for any new development platform, driving dramatic changes in the design process.’
Performance matters
With such widespread demand across industries both old and new, an increase in computational performance is required. Krishna said: ‘Low-cost computers are being replaced by laptops and the availability of inexpensive memory have made it possible to solve and optimise larger problems faster than before. Moreover, FE software has gone through multiple iterations of enhancements to take advantage of computer hardware improvements.’
Cloud computing is one such improvement, which is growing steadily thanks to the cost-effectiveness of this technology. Alan Prior, senior director of technical sales EuroNorth at Dassault Systemes, said: ‘Access to simulation on the cloud is a major growth driver. No longer do companies need to invest in their own HPC and platform infrastructure. On-cloud access to both software and platform-as-a-service is expanding access and value from a company’s investment in simulation.’
One of the biggest changes has been the delivery of FEM technologies embedded into a broader simulation framework, according to Prior, who said: ‘No longer is there a requirement for customers to purchase a solver, a pre-processor and a post-processor, and no longer do analysts need to run a different product for each of the physics domains they want to simulate. Today, we offer a broad range of technologies in a single environment, the 3DExperience Platform, connecting the CAD and design tools, connecting to the visualisation tools, and covering an extraordinarily wide range of physics.’
‘As a result, our customers have found that investment in virtual simulation – available 24/7/365 – pays significant dividends in getting better products to market faster and cheaper than by just relying on physical testing alone,’ Prior added.
Moving to multiphysics
This is where multiphysics simulation picks up the baton for the FEM in order to enable more use cases and users.
For example, in 2014, Comsol took a step forward in the democratisation of simulation by introducing the ability to create simulation apps with its Application Builder in Comsol Multiphysics and the launching of the Comsol Server product.
Sjodin explained: ‘The Application Builder is integrated with Comsol Multiphysics and enables simulation specialists to take their multiphysics models and turn them into specialised easy-to-use apps, perhaps having just a few buttons and input fields. The simulation apps allow those who are not specialised in simulation to reap the benefits of simulation. Comsol Server is our web-enabled deployment platform for apps. Users can install the Comsol Server software locally or at a central location in their organisation, or even in the cloud, to let anyone on their team, or even customers, access the apps.’
Sjodin added: ‘The Application Builder and Comsol Server were developed to address the bottleneck in the industry. In many organisations, small groups of simulation specialists work with larger groups of individuals in product development, design, and manufacturing. Multiphysics models are oftentimes so complicated that the simulation expert is the only one who can safely run the model, even if it is a single parameter that the design team is interested. With the Application Builder, the simulation expert can create multiple apps based on a single multiphysics model to empower individuals throughout the company to test different configurations for their particular requirements and pick the best design.’
Comsol is not alone in this space. For example, Dassault Systemes has a 40-year history of providing FEA technology and products, including in-house developed solvers and the Abaqus suite, which it acquired in 2005. Prior said: ‘The Abaqus tools remain a strong component of the Dassault Systemes portfolio, but we’ve extended our offer significantly: today, we offer a complete Multiphysics-Multiscale framework on the 3DExperience Platform that provides our customers the ability to solve end-to-end industry workflows in 12 Industries and 70 segments.’
While none of the products’ functions in the Wolfram Language are based solely on the FEM, it is used to extend and complement other partial differential equation (PDE) solving methods. For example, for stationary and transient PDEs there is NDSolve and, for eigensystems, there is NDEigensystem. Also, numerical integration can be performed with the FEM (using NIntegrate) and interpolation of functions (using InterpolatingFunction) can be done with the FEM.
Altair has also increased the emphasis of multiphysics solutions, as Sampson explained: ‘Multiphysics is one topic that’s advanced dramatically over the years, the need to simulate and analyse different types of physical phenomena within one model. Much is driven by solver coupling, for example electromagnetics (Flux) and structures (OptiStruct), but also the need from the pre- and post-processing perspective is important, the need for multiple products to exchange data correctly is vital.’
Consequently, the integration of a large number of third-party applications and vendors continues to increase. Sampson said: ‘Reducing model build times is critical. Models are continuing to increase in size and complexity which requires new tools within the pre-processor whether it’s HyperMesh, SimLab or Inspire. Streamlining model build processes by improving the product user interface and embedding engineering process within the tools is now standard.’
Future challenges
However, the real challenge for the continued advancement of the FEM does not lie with the technology, as Prior explained: ‘With 40 years’ experience in developing FEA technologies the most significant challenges are not in the internal technical work.’
Prior said: ‘In fact, the major challenge might be termed ‘institutional inertia’. Many companies are hardwired with the thought that product design requires extensive physical prototyping. They test until the prototype breaks, then redesign, make another prototype and retest. That’s a hugely inefficient and time-consuming process, with no guarantee that the final design will be the optimal one.’
‘Certainly some prototype testing is essential, particularly in validating the simulation methods. However, the virtual testing provided by simulation can significantly reduce the number of prototype test cycles and thereby shorten the time to achieve an optimal final design.
‘We need to promote the value that simulation brings as an intrinsic part of the product design process, to help companies realise the commercial benefits that it brings,’ he added.
In other words, these benefits need to be demonstrated to a wider range of industries to further the reach and advancement of FEM techniques. Sampson explained: ‘[A key challenge is] to ensure Altair’s products remain as an open architecture platform applicable for all industries and domains. However, sometimes a specialised product offering to target a specific audience is required and as such the integration and cross-platform communication with other existing products is necessary.’
Sampson added: ‘Furthermore, since our customers are experiencing a more-than-ever compressed time-to-market for their products, we need to quickly respond to market trends. The trend may not necessarily be in the context of FEA but in the context of engineering and making sure we deliver the appropriate quality solution to address the market.’
Krishna added: ‘The time to solve a problem increases with the increase in the number of details to be modelled. For example, a bolt can be simplified as a 1D or 3D representation.
‘The 3D representation can further have multiple forms. The thin solid can be modelled as a sheet. The modelling detail can include multiple physics that govern the problem or study only using the dominant physics.’
‘But the product developed should be designed for its users [and] the FE products have gone through a facelift to improve usability and handle large complex models. The younger generation is more comfortable with the internet and hand-held devices, which is changing the way software, training and documentation are delivered,’ Krishna added.
This ‘FEM for all’ ethos has revolutionised the way simulation solutions are presented. Prior explained: ‘Customers want simulation to be available to inform decision-making everywhere in their companies, not just in the engineering department. That means that the results of the simulations need to be available to a wider audience and in a range of formats that can be interpreted by both specialists and non-technical people.’
‘In order to improve scalability, many customers want to ‘record’ the methods built by expert users and make these methods available for non-specialists to use as part of the product design and development process. This kind of process automation or analysis templating approach is becoming an important requirement,’ Prior added.
Automation and the integration of machine learning technologies is one way to simplify the modelling process, as Sjodin explained: ‘I think FEA will find new ways of making it easier to access the technology. Apps are one way, perhaps there are more ways the industry hasn’t thought of yet. Artificial intelligence is on the rise and there may be opportunities to further enable access to simulation through this technology.’
Krishna concluded: ‘The complexities of modelling systems that involve multiple physics is still a challenge. Besides the fundamental difference in physics, there are modelling practices differ significantly from one domain to another. Bringing them all into one software can be difficult if not impossible.
‘Multiple FE products will be used to solve different problems but these will be coordinated/integrated by a simplified user interface that couples the different products. Many verticals will be in use to address specific needs. They will be interactive and will respond in real time. Improvements in computers and machine learning will simplify the modelling process.
