Can anyone explain me, what is the importance of jacobian check and secondly what is meant by 4 points, 16 points, 29 points or at nodes options in mesh settings?
The jacobian check is used when your mesh is a "High Quality" mesh e.g. parabolic 2nd order elements; meaning, they have nodes at the end of each edge as well as one mid-side node on each edge, these mid-side nodes can wrap around geometry such as high curvature regions much better than a linear "Draft Quality" mesh can accurately capture those regions of your model.
This does mean that with "dirty" geometry like tiny little edges or small sliver faces (think for example a V-notch kind of shape) can cause the mesher to place mid-side nodes in such a way that they make the Jacobian a negative number. Which all you really need to know is: Makes the solver fail!
Are you familiar with the COSMOS Companion? It kind of like, totally kicks ass! I think if you Google it you should still find a few .pdf versions floating around the internet, it goes into the details of SolidWorks Simulation on various topics, including one that mentions this option.
Basically, what it says in there is that there is no real hard evidence that using any more than the default amount of points for the Jacobian check makes it much better.
I agree with Kevin. The default setting is usually fine. The way I understand it, the algorithm evaluates the deformation of the element by evaluating a volume integral at special points in side the element - the more points, the better the evaluation, but again I have read the default setting is ok. A deformation parameter is that the element not be folded-in on itself. If meshing highly curved geometry, you can visualize (as Kevin pointed out), a mid-side node placed on geometry can cause an element edge to "kink" too far. It is written somewhere that if the elements are too deformed, they lose accuracy very rapidly. Hence a desired element shape should be as "equilateral as possible", implying straight sides. Anyway I also read somewhere that the maximum "Jacobian" value is about 40. You can plot the "Jacobian" if you create a "mesh plot" (right click on the mesh icon to see that), and the two options are "Aspect Ratio" and "Jacobian". Keep aspect ratio under about 5 for structural (that's just a ratio of longest normal to shortest normal in an element, where a normal is dropped from a vertex node to opposite face of the element), i.e., a measure of how 'stretched-out' the element is.
It has been my observation that the jacobian setting does not influence the mesh you get or the time it takes to get it (at least not noticeably) but it does increase the precision/resolution of the computation of the jacobian value. I use 29 point as my default.
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