Making the optimal grade

Researchers in Vietnam and Canada have developed a ready to use model to predict critical loads for functionally graded materials. Their neural network-based technique is ideal for users working on functionally graded plates and does not require advanced coding skill to implement [Le T-T, Duong HT, Phan HC. Optimization of Neural Network architecture and derivation of closed-form equation to predict ultimate load of functionally graded material plate. Advances in Mechanical Engineering. 2023;15(5). doi:10.1177/16878132231175002].


Making the optimal grade
Researchers in Vietnam and Canada have developed a ready to use model to predict critical loads for functionally graded materials. Their neural network-based technique is ideal for users working on functionally graded plates and does not require advanced coding skill to implement [Le T-T, Duong

Functionally graded plates
Functionally graded material plates are, generally, a mixture of ceramic and metal, and are designed to exhibit the strengths of each constituent, while, concomitantly, each constituent compensates for the weaknesses of the others. For example, ceramics are extremely stiff and resistant to problems associated with heat. but they are brittle. Metals tend to suffer under extreme heat changes, but their ductility compensates for the brittle nature of ceramics.

Predicting behaviour
As composites, functionally graded plates (FGPs) are more complex to manufacture and to model than more plain structures, which is especially problematic, given their wide range of uses in any number of applications. Analytical models exist, but the complex nature of FGPs mean that numerical approaches are necessary for real-world applications: the analytical models are extremely advanced and thus computationally very costly.
One alternative method is to use a data driven approach, combined with machine learning techniques, such as artificial neural networks (ANN). The finite element models required for such an approach are, unfortunately, far too massive to be practical, and the required ANN architectures are extremely difficult to define.
Given that FGPs are so universally applicable, understanding their load limits is paramount, and this is where the authors have turned their attention.

Analytical versus numerical versus learning
In the present work, the authors have developed a hybrid approach, part analytical, part data driven, which simplifies both the required ANN architecture and reduces the cost of the analytical model. The authors use an ANN to derive an equation that users will be able to incorporate into their own work to predict the load limits of FGPs. They have also provided a look 'behind the scenes' of the ANN, along with a convenient, GUI-based tool.
Their optimised ANN reduces errors in both training (ANNs have a training layer, a crucial part of their operation) and testing datasets, reduces workload on memory, and the final results are more accurate than previously reported. The computational speed is also drastically increased: over 300 times faster than existing techniques.

The results
The results are impressive when validated against existing analytical models, and the computational time savings are significant, but the authors have also shown that their technique can be used to optimise the properties of FGPs ahead of time, reducing the need for costly testing and simulation.
The report of the authors research makes fascinating reading and provides an overview of the existing state of the art. It also serves as a great starting place for anybody interested in this fascinating subject: the references and clarity of explanation are instructive for any beginner. Moreover, it's a perfect example of a simple but difficult idea that can be used by the wider community to enhance, not only applications, but also their own fundamental approach to research.

Declaration of conflicting interests
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.