In the previous post, we saw that results delivered by meshless techniques, such as ReveaL, are within 1% of those that standard finite element software compute. When the geometric model and the material parameters are identical, this is not a surprising result. It is not surprising because the technology behind ReveaL builds upon the same mathematical foundations as standard finite elements. As pointed out in the comments on our first blog post, when we start from a clean CAD model that mesh generators are able to digest, meshless methods might fall behind in terms of sheer computational time. However, as the quality of the CAD model deteriorates, ReveaL’s shine gets bigger and bigger. But what happens if there is no CAD model at all to start with?
We are so much used to the fact that every analysis starts from a CAD model that we forgot about a tiny question. What happens even before the magic mesh generator button is clicked: what if the object we want to simulate doesn’t have a CAD representation at all?
Think about it. Many things in the world around us were designed by mother nature instead of an engineer: the bones in our body, rock formations, landscapes, riverbeds, all things with interesting physics yet impossible to simulate directly. Further, a digital model might be missing even if a human-designed the object. Prominent examples for this case are from the world of cultural heritage. Statues or historical monuments for example are human-made structures without a CAD model. When we want to simulate them, someone needs to do a complete re-modeling before even thinking about generating a mesh. This reverse engineering is a time-consuming process.
If the object is simple, like a cube made of stone, it is easy to re-model it. Take a ruler, measure one edge, make a cube in CAD, done. But what happens if we need to reverse engineer the model from the previous post?
Using a simple ruler, reverse engineering this model will take forever. Thankfully, there are alternative techniques that make our lives easier. There are coordinate measuring machines that rely on mechanical contact between a probe and the object. There are also contact-free measurement techniques, e.g., laser scanning of photogrammetric reconstructions. The common feature of these shape measurement methods is that their output is a bunch of points representing the object’s surface. They are usually called as point clouds.
While a point cloud might spare the time of measuring the surface of an object, it does not help the analyst further at all. There is no way to generate a mesh directly on a point cloud without first turning it into a surface model. There are different ways to recover a surface model. However, many of the recovered models are full of flaws that prevent analysis in the first place.
In a previous project, our client recorded a surface scan of the cast aluminum part that we investigated in a post in the past. They started turning this into a surface model when we were asked to have a look:
It is clear that before standard finite element analysis, there is a lot of clean-up to be done before mesh generation can take place. We thought that this is a great opportunity to test the capabilities of ReveaL, especially that we have a reference result computed on the original STEP model. So we set the goal to perform a modal analysis just like in the previous post, but this time on the surface scan. This will make it possible to make a three-way comparison on the reference computed by a standard CAD tool and our results from the standard geometry and the surface scan.
Therefore, we loaded the surface scan in ReveaL and performed a modal analysis. As always, let’s start with the colorful pictures about the first three eigenmodes, comparing ReveaL and the reference result:
First eigenmode, ReveaL on surface scan and reference solution
Second eigenmode, ReveaL on surface scan and reference solution
Third eigenmode, ReveaL on surface scan and reference solution
Just like we did before, we compared the values of the first 9 eigenfrequencies in a tabular form:
|Eigenmode||Eigenfequency ReveaL on surface scan||Reference solution||Difference|
|#1||742.782 Hz||744.85 Hz||0.27%|
|#2||805.674 Hz||827.87 Hz||2.68%|
|#3||1309.51 Hz||1310.83 Hz||0.1%|
|#4||1380.75 Hz||1406.44 Hz||1.83%|
|#5||1542.1 Hz||1542.16 Hz||0%|
|#6||1786.01 Hz||1748.12 Hz||2.17%|
|#7||1985.97 Hz||1944.03 Hz||2.16%|
|#8||2385.65 Hz||2317.98 Hz||2.92%|
|#9||2554.06 Hz||2503.14 Hz||1.7%|
As seen in the table, every eigenfrequency stays within 3% of the reference solution. This in my opinion is quite good for a method that spares about 80% of the preprocessing time!
Yes, it is! It turns out that there is no need to reconstruct any surface from the point cloud. Instead, it is enough to feed ReveaL with the point cloud directly. In the upcoming weeks, we will have a look at examples where not even a partial reconstruction is available, and the analysis is performed directly on the cloud. Stay tuned!