Today’s naval architects face ever-increasing distractions with modernity.
It seems that with increasing computing power, the allure of using programs like finite element analysis (FEA) for structural analysis is beyond commonplace; it is a must. Advertisements by software companies highlight the ease with which complex structures can be analysed, making it difficult to ignore, for most at least, anyway.
The seamless transition of creating a model in one software to then importing the model into the same or another software to begin the process of analysing the structure via FEA looks like child’s play. In fact some software programs do all the work for you. All one is required to do is press the buttons and presto! The answer is provided!
If it were only that simple.
So, what is FEA, and when should we use it? Is it even worth bothering with hand calculations, since everything in the modern design office is performed using these ever more powerful computers inside a digital environment?
Let’s address the basics. The finite element method is a mathematical method that can be used to obtain solutions to complex engineering problems. The analytical solutions to problems in general require the solution of ordinary or partial differential equations that, because of the complex geometries, applied loads and material properties, are too complex to be solved using hand calculations.
The concept behind the finite element method is to find the solution of a complex problem by replacing it with a simpler one. In reducing the problem to a simpler one, an approximate solution rather than an exact solution is obtained.
Without getting too detailed and complex, it can be broken down into two basic approaches. The first, the principal of virtual work, is the most fundamental tool for the analysis of statically indeterminate structures; it also has the advantage of being able to deal with conditions outside of the elastic range.
The second is based upon strain energy that can provide solutions of complex problems for which exact solutions may not exist. So, in this simple breakdown, if this is starting to sound like a university lecture, then good! Since most users simply plug and play and “assume” everything is correct, why, because it is FEA, it must be correct. Nothing could be farther from the truth, however.
Without a background in structural analysis using matrices and higher degree polynomials, it won’t make any sense.
The objective of FEA is to accurately determine the response of a system modelled with finite elements given the applied loads and boundary conditions. But since we now know that FEA does not provide “exact” solutions, how can we trust it? This is where the link between mathematical modelling using the finite element method and the physical world – by addressing the constraints and methods of modelling in order to provide more accurate solutions that can be verified by experimentation – come into play.
Selection of element types (2D or 3D how many degrees of freedom, etc), the application of loads, as well as the manner in which the model is restrained to reflect the true physical model all have an influence on the results obtained. It is therefore vitally important that the user of such software can understand these limitations as well as the effects of such that are required in order to provide results that are consistent and verifiable.
Again, in simple terms, try modelling a simple beam as a flat bar that is structurally built-in at one end and a simple point load is applied at the free end.
The chances are that a first-time user of such software, or indeed, perhaps even a more experienced user, would find that the results obtained by the FEA do not match that of a simple hand calculation. This then begs the question, “Why not? what is wrong?”
And this is the whole point. Without a background in structural analysis using matrices and higher degree polynomials, it won’t make any sense. The way the model is restrained (held) has a major influence on the result, as does the means in which the force is applied to the model – at one node at the end, maybe? Just like the simple structure drawing, and not forgetting the all-important type of element used.
This goes down an even more complex discussion on shape-functions. All structures deform under load, and whether the shape of deformation can be created mathematically via higher order polynomials is the basic premise. This is not basic algebra.
The above is merely scratching the surface of a very complex use of mathematics to solve very complex problems using even more complex concepts of mathematics. The more one delves into the theory, one realises that it is not as exact as one is led to believe.
Hand calculations win hands down.
So, we go back to the beginning. Given what we now know, that FEA is not so straightforward, does not provide exact solutions, requires a deep understanding of how elements behave (no two are alike) – unless one is extremely well versed in knowing how to “guide the model” – and the time taken to manually create the model and mesh (not using the automatic function), when done correctly, would it be worth it? Well, it is a fair point.
Yet it is so easy to be beguiled by adverts and social media posts by users showing how wonderful the colour plots can be and the simplicity of clicking from a model into the FEA side, thus providing an instant answer. Some of the software programs available offer very little regarding the means to control the FEA; that would otherwise yield an exact solution, or very close to it, once one understands the theory of FEA. But of course, why let facts get in the way of a sale or a colourful promotional plot of a complex structure?
The simple bottom line is this. Any complex structure can, with experience, be broken down into very small simple beams, like a simply supported or built-in beam. Having the ability to recognise how to break down a complex structure into a series of “simple” beams may not be an “exact” solution (sounds familiar?), but it is a solution one can trust and verify, and this is a skill in itself.
It may be considered to be over-engineered. However, also factoring in the time to arrive at an answer in order to establish whether a structure is safe or not, and to do so within a production time scale, is far more valuable. Hand calculations win hands down.
If this seems like a negative dig at FEA, it is far from it. Rather, it is a cautionary tale that using such powerful software is not as simple as, “press the button and go”. It requires training and understanding the theory behind it far beyond the sales blurb in the user manual.
Having used FEA for over 30 years, I still do not profess to know everything about it. However, what I do know is how to control the model manually, not relying on automation and selecting the correct element types and applying the boundary conditions and loads, in a manner that is “consistent” and yields a result that is offering an idea of what one should expect the structure to behave like (supported by simple hand calculations) and thus plan mitigation accordingly.
It is not an absolute, but an indication of what is kind of likely to occur.