As a species, we do few things better than innovate. From the transition from the horse-drawn cart to the steam engine to lighting homes with electricity instead of candles – the history of human beings is rich with examples of us developing new, enhanced technologies for the betterment of all.
Right now, a similar process is taking place in the world of mechanical engineering, with the development of a game-changing new engineering simulation software called Reduced Basis Finite Element Analysis (RB-FEA).
What is RB-FEA?
Before we get to RB-FEA, we need to back up and look at what came before.
As any mechanical engineer knows, Finite element analysis (FEA) is a widely used numerical method in engineering and manufacturing to predict the behaviour of complex systems under different loads and boundary conditions. FEA is a powerful tool that allows engineers to simulate a system’s stress, deformation, and other physical properties without requiring expensive and time-consuming physical testing.
However, while FEA has its strengths, it also has its limitations, particularly when analysing large and complex systems. RB-FEA (Reduced Basis FEA) is a newer method that builds on the principles of FEA but offers several key advantages.
These advantages are based on the fact that RB-FEA is a “reduced order modelling” (ROM) approach, in which a “reduced basis” that represents the response of the system is automatically generated (based on an adaptive “training” process that leverages FEA at the sub-system level).
This approach yields a condensed mathematical representation of the system being solved while also ensuring accurate results based on physics-based accuracy indicators that drive the “training process”. This leads to a fast and scalable simulation method with guaranteed accuracy.
How Does RB-FEA Improve Upon FEA?
Speed (with Guaranteed Accuracy)
One of the advantages of RB-FEA is that it is inherently much faster than FEA. The number of “degrees of freedom” in an RB-FEA simulation is typically 1/1000th of the corresponding FEA solve, which leads to orders of magnitude speedup compared to the conventional approach.
Many ROM methods, including machine-learning-based methods or response surfaces, can provide fast results. However, what is unique about RB-FEA is that it is quick and provides guaranteed accuracy.
The guaranteed accuracy stems from the academic literature on reduced basis methods, in which there has been extensive work to develop accuracy indicators. These indicators will specify if an RB-FEA solve satisfies a specified accuracy threshold. If that threshold isn’t met, the RB-FEA ROM can be automatically enriched further until the threshold is satisfied.
In practice, this means that we can use RB-FEA as a “drop-in” replacement for FEA to obtain a significant speedup while still ensuring that the complete accuracy of FEA is achieved. Indeed, in many cases, RB-FEA allows the user to surpass the accuracy achievable in practice with FEA because the speedup makes it feasible to use much more refined computational models than would be possible with FEA. In contrast, FEA often necessitates coarse meshes while limiting the analysis’s accuracy.
One caveat to the RB-FEA’s speed is that we can only model some physics types with this ROM approach. Typical examples that RB-FEA does not handle are plasticity and contact. In such cases, a small perturbation in loading can lead to a discrete change in the plastic or contact fronts, making it infeasible to apply standard RB-FEA reduction methodology.
Akselos provides nonlinear FEA solvers to handle these types of cases and a unique “Hybrid Solver” that includes both RB-FEA and FEA regions within a single solution, in which nonlinear FEA is used in areas where it is needed, and RB-FEA is used elsewhere. In practical cases, the Hybrid Solver often leads to a 100x speedup compared to FEA because we often encounter localised plasticity or contact in industrial models (e.g. localised failure or localised contact).
Finally, we note that the speed of RB-FEA opens the door to applications that are not possible with FEA, such as real-time monitoring of large systems or design studies that require thousands or even millions of solves.
Scalability to Large-Scale Models
Another of the advantages of RB-FEA is its scalability to large-scale models. The same DOF reduction that leads to the speedup discussed above also leads to the ability to solve much larger models with RB-FEA than is practical with FEA. We have demonstrated this by generating RB-FEA models equivalent to over 100 million FEA DOFs and still solvable in seconds.
A key point in the scalability is that Akselos’s technology for automatically training RB-FEA never requires us to solve a global FEA model since all training computations are done on local sets of components. This means that we can solve extensive models via RB-FEA without ever needing to solve them with FEA, which is a true game changer in model size that can be solved in practice.
Parametric ROM Enables a More Thorough Analysis
Finally, another of the advantages of RB-FEA is that it enables more detailed analysis.
RB-FEA is not just a ROM; it is, in fact, a “parametric ROM”. This means that an RB-FEA model includes parameters that can be used to modify and resolve a model quickly without requiring any update to the RB-FEA model itself. Typical parameters are material properties, geometry, loads, or temperature. These parameters are taken into account during the RB-FEA training phase. Hence, the RB-FEA model will accurately represent the response for any new value of a parameter used during “online” solves (again with guaranteed accuracy due to the accuracy indicators discussed above).
Parameters are a powerful feature of RB-FEA that enables users to update a model in real-time to match sensor measurements or explore an entire design space by efficiently solving thousands or millions of different model configurations.
Conclusion: RB-FEA is an Increasingly Popular Choice
As demonstrated above, RB-FEA provides several key advantages compared to FEA. As a result, it is becoming an increasingly popular choice for engineers and manufacturers looking to simulate and predict the behaviour of complex systems.
Akselos, a leading provider of RB-FEA solutions, is at the forefront of this technology, developing cutting-edge solutions for engineers and researchers. With Akselos, engineers and asset owners can apply RB-FEA in operational environments and work more efficiently, make better decisions, and achieve more valuable business outcomes. Our software can also be linked to data from sensors on the asset to create a structural digital twin, such as the world’s largest digital twin of the Shell Bonga Floating production storage and offloading unit (FPSO).
If you are interested in learning more about how this technology can help you reshape your industry, we’d love to hear from you.TALK TO ONE OF OUR EXPERTS