Simulate Early, Simulate Often... In Rhino
Scan&Solve uses a finite number of elements to analyze the object. The resolution refers to the number of elements in use in the solution grid. A resolution sufficient to show the small changes in geometry should be chosen. This reference shows the effect on the results when a small resolution (relative to the geometry) is chosen. The distribution of these elements in Scan&Solve can be viewed with the Show Grid option.
In general, increasing the resolution of a simulation will increase the accuracy of its results. However, changing the resolution can cause the results to fluctuate because the distribution of the solution grid changes. To account for this, a comparison of the results should be made at several resolutions. This process is known as convergence checking.
A common test of finite element software is to study a problem with a known, mathematically obtained solution. While the numerical result may not agree with the mathematical result at low resolution, the numerical results should approach or converge with the mathematical solution as the resolution is increased.
The following example shows the results of analyzing a hollow cylinder with a distributed load and fixed ends. Beam theory predicts a maximum deflection of 2.83mm.
Link to model: HollowCylinder.3dm
The data in the following plot was generated using SnSScript. The deflection converges to the expected value and does not fluctuate much as it approaches the expected value. Note that there are a few outliers at very low resolution. These outliers are why it is important to check the convergence of a solution value.
In some cases, a solution may never converge. This is the case for the following example: a wedge has an edge restraint placed on its tip, with a load placed on the other end. Because the model is only restrained along a single line, the wedge tip can deform around the restraint. This means that increasing resolution will continue to increase the stress.
Link to model: Wedge.3dm
The phenomenon can be seen in the graph below. The von Mises stress does not converge onto a particular value: it continues to increase as the resolution increases. This effect is actually a result of linear elasticity: stresses (force / area) become infinitely large as the area approaches zero.
Because the value of stress does not stay steady around a particular value, it is non-convergent. In addition to the generally increasing stress, the stress values tend to oscillate. The stress oscillations occur because the solution is sensitive to changes in the distribution of elements. This behavior is expected for the particular geometry, but will not occur often in most models.
The following graph shows the maximum displacement results for the wedge. Like the hollow cylinder example, the displacements converge to a particular value. In finite element analysis, the displacements are the fundamental results of the simulation and tend to converge at lower resolution than stress and strain values.
In all of these plots, there are distinct outlier values. If, purely by chance, a resolution is chosen that produces one of these outlier values, then the results are not representative of the problem. These numerical outliers represent one of the faults of numerical analysis and the necessity of convergence checking.
For most geometries, there is not an expected value that can be compared to. Instead, when checking for convergence, the solution value of interest should be checked against the result at another resolution. If the solution value has changed significantly between the runs, then the resolution should be further revised until there are only small changes in the value of interest.
Automated convergence checking can be performed using SnSScript. This page provides a script to do so. Also included on this page is a script for producing the plots seen above. The script produces a CSV file, which can then be plotted in a number of programs (for example, Excel or Google Sheets).
Thanks for reading,
Will
Further Reading
How to select a resolution for analysis
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The basic mechanical analysis software needs to mesh with different elements (tetra, hexa....etc) for getting simulation results but how I can confirm this scan&solve simulation results will match with ANSYS or Hypermesh results.
Generally speaking, this kind of benchmarking requires setting up identical testing conditions and assumptions... which may defeat the purpose of the whole experiment. For example, Scan&Solve enforces the restraints over the faces, and not just at the mesh nodes, does not require defeaturing and simplification, etc. Why would you even expect to get the same answers? But, if it is really important to *you* then you can create identical conditions and run the tests and comparisons yourself ... or you can rely on the tests performed by other users, e.g. read this post
Thank you, may I know which meshless method is using for this software and explain the solvers (SNS, ISS, DSS)
Comparison of Scan&Solve and classical FEA can be found at this page, where you can also find the link to detailed technical paper. A popular introduction written some time ago can be found here.
You can find brief description of solvers in the documentation under settings. Briefly, DSS is a direct solver that is very fast but requires large amounts of memory; SNS and ISS are iterative solvers which could take longer to converge to the solution, but they allow solving much larger models (i.e. at much higher resolution).
I read the scan and solve based journal papers but how I confirmed the solution is converged and I observed that when changing resolution (i.e elements) automatically the results are changing so what it means?
published papers: SCAN AND SOLVE: ACQUIRING THE PHYSICS OF ARTIFACTS, ASME conference
will you suggest any published papers related to femur bone or skull with the use of scan and solve software?
SCAN AND SOLVE: ACQUIRING THE PHYSICS OF ARTIFACTS
The best reference is probably this journal paper. We are not aware of any specific studies related to femur bone or skull. Of course, every application is different, but the principles of using FEA are pretty much the same.
Well, your software is awesome especially for structural analysis of CT bone data but how I conclude the results are pretty good.
If mesh file is having any error (not a water tight model/closed surface) can this software simulate the model? In traditional FEA software need closed surface otherwise it can't mesh.
We agree that our software is awesome for structural analysis :-)
Please see the documentation that lists which models in Rhino are supported. If Rhino thinks that the model is solid, then the model is good enough for SnS.
Well, I tested the CAD model in Ansys and SNS software bothe are same as per stress distribution but the output numerical results are not equal, somehow I am very happy with this software.
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