Jacobian

[kapmnit123]

Dear Experts,

I have a bit of confusion regarding jacobian interpretation in finite element analysis.What does Jacobian signifies? Is this just a transformation matrix between two sets of co-ordinate systems or is it a measure of the deforamtion (streching/shearing) of a mesh element?

Any particular citation for reference?

Regards

Kapil Sharma

 

[KevinDeSmet]

This may be helpful:

http://blogs.solidworks.com/solidworks_uk/2009/08/confusing-terminology.html

Now if you'll excuse me, I'm going to put on my flame suit from all the real analysts who think Solidworks Simulation is just a toy

Certified SolidWorks Professional

 

[kapmnit123]

Hi Kevin,
Thanks for your reply.It was a good practical explaination of what i asked for.
My question was bent more on the academic side of FEA..Jacobian matrix is used for transformation between global and natural co-ordinate susytems (isoparametric elements) so does that mean that the determinant of this matrix and the jacobian (as stated in the blog article you refered) are same????
Regards
Kapil

 

[cloa]

http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

This would indicate yes.

 

[btrueblood]

A bigger issue in the bad old days of self-generated meshes, was getting a negative Jacobian, indicating that you had inverted the numbering convention for a given element (i.e. the numbering violated right-hand rule convention for the element's coordinate system).

You don't see it very much any more for typical automeshers, but...if you have weird geometries, with multiple hollows and reentrant curves...you'd be surprised at the error messages you can see.

 

[kapmnit123]

hi thanks all of you.
Regards
Kapil

 

[bxtsafe]

Hi everybody!

No... the determinant of an element's Jacobian Matrix is not the so called "Jacobian" found in the FE sofwares. Although wikipedia says this, there is a little difference when we're talking about the Jacobian in the Finite Element Method.

Please, take a look at the post Meaning of Jacobian in FEA for further information.

Regards,