One of the parameters driving the age old question of “is my mesh refined enough?” is the impact it has on the model size and the knock-on effect to runtime and computer spec. This comes into starkest relief if you have a dimensionally very large structure but where you need a fine local mesh around some detailed areas in order to refine stress intensity for e.g. fatigue life prediction.
Almost all the solid element meshes I come across in the last decade or so have used second order 10 noded tetrahedral elements, and for most applications they are perfectly fine. There are however some applications in some FEA solvers that require a hex8 element – for example some elastomer models, magneto and electro static solvers and some acoustic solutions. How do you mesh an irregular part in hex elements?
It is for good reasons that designing laminated composite structures is sometimes known as a ‘black art’. It is not easy to intuit from the topology of and loads applied to a component what a good ply layup should be. Many companies rely on the wisdom of veteran engineers’ hard won experience, but sometimes it is necessary to take a step back and ask “what else could we try?”.
Often the design of a composite layup starts with the definition of zones within a part. The layup on each of these zones can then be fettled using FEA to arrive at a stacking sequence which can then be used to define plies.
But how do you choose the zones? Is it arbitrary based on the topology of the part? Do you just chequer-board your panel into regular squares? You could use a technique developed with MSC Nastran for one of the F1 companies.
Modelling Cracks the Easy Way
In my previous blog I talked about the advantages of automatic re-meshing in the analysis of rubbers in improving accuracy and stability of a simulation. One advanced application of this capability that was not touched upon was in the field of crack propagation.
In many industries it is sufficient to use your analysis to predict that a crack could initiate and redesign the part to avoid this occurrence. In others though it is possible that a crack may be identified from an in-service inspection whereupon it becomes necessary to understand if it will propagate under the loads applied and how quickly so that a replacement can be introduced in a timely manner.
Predicting crack growth in materials with finite elements can seem more art than science.
As an example, in some codes you may need to construct a very precise ‘rosette’ mesh at the crack tip.
A series of angular perturbations to the crack tip node are then simulated to look at the energy release resulting from extending the tip with the assumption being it moves in the direction of the greatest energy release.
Coping with Large Strain and Large Deformation in FEA
One of the challenges of analysing the performance of large strain materials like rubbers and synthetic elastomers is how the finite element mesh distorts as the part deforms. You may well start out with a lovely mesh where all your elements meet your quality standards, but as the part distorts the element quality gets worse and worse until it can actually prematurely end the analysis because of excessive distortion, let alone give you poor results.
This is not an uncommon problem.
In a previous article I discussed using random analysis to predict failure of components in a vibration environment. Random analysis is a quick way of ensuring that statistically the maximum stress due to a vibration loading will not exceed a set level, but the most common mode of failure in such an environment is not due to one single load spike but due to the summation of damage from all the load cycles – known as fatigue failure.
Classically fatigue failure due to a transient load was performed quasi-statically. A known load history was combined with stresses from a unit load in the FEA model to create a stress time history. Rainflow cycle counting was used to evaluate the stress cycles and then damage calculated from these using classical theories like Goodman and summed using Miner’s rule. There were problems with this method though.
The use of FEA to design ‘optimal’ components has been around for nearly two decades. In general terms it works by meshing an available volume for a part and then eating away at the space iteratively to leave just those bits of the mesh that are doing work while aiming at a target mass for the part, as in the examples below.
Using this method ‘raw’ it is easy to see how un-manufacturable designs can result, so much effort has been invested by software developers to place manufacturing constraints on the optimisation process to, for example, eliminate voids or undercuts in moulded parts.
In an earlier article I talked in general terms about the benefits of using CAE tools to model the physics of manufacturing processes. In this article I will show a case study example using welding simulation to decide on the best strategy for welding a two-part swing arm together.
The objective is to compare two different clamping schemes with third iteration that uses tack welds to hold the parts together.
The two parts were made of carbon steel, welded along an ~80mm length using arc welding with an estimate energy input of around 2000J per centimetre.
The simulation tool used for this analysis uses a state-of-the-art multi-physics finite element programme as the underlying solver, but has a custom user interface that speaks to the manufacturing engineer about his process flow and not about the minutia of an FEA job set up.
Working with long duration transient events in a finite element world can be extremely computationally expensive. If those events are very long, like the wheel hub forces over the lifespan of a vehicle, then it is impossible to simulate. One technique to overcome this limitation is to use something called Random Loading, or Random Analysis.
If a time signal can be considered properly random then it can be transformed from the time to the frequency domain and is known as a Power Spectral Density plot, or PSD. A quick check of randomness is that any section of a time history transformed in this way should give the same outcome as the whole signal. These PSD’s are best thought of as a statistical representation of the amount of energy in the signal as a function of frequency.