Jacobian
Altair EmployeeHello,
I'm a currently starting with Hypermesh. While going through the tutorials I found the topic 'elements check'. Within this topic the term Jacobian crosses my path frequently. However, no exact explanation about it is given nor why it should be lower then 0.7. Could anybody tell me what the Jacobian term represents, where this 0.7 comes from, etc?
Thanks!
Answers
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I copy from HM help file. If you have the document cd, search keyword jacobian, then quite a lot of results would show up.
This measures the deviation of an element from its ideal or 'perfect' shape, such as a triangle’s deviation from equilateral. The Jacobian value ranges from 0.0 to 1.0, where 1.0 represents a perfectly shaped element. The determinant of the Jacobian relates the local stretching of the parametric space which is required to fit it onto the global coordinate space.HyperMesh evaluates the determinant of the Jacobian matrix at each of the element’s integration points (also called Gauss points) or at the element’s corner nodes, and reports the ratio between the smallest and the largest. In the case of Jacobian evaluation at the Gauss points, values of 0.7 and above are generally acceptable. You can select which method of evaluation to use (Gauss point or corner node) from the Element Check Settings window.
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the jacobian is a transformation matrix. in FEM, it maps the fe elements in the real world and the elements in a world that is a square of 2 by 2 (from x=-1 to x=1 and y=-1 and y=1). (depeding on the formulation). 0.7 is a good index to avoid numerical errors.
you should review you solid mechanics and fe books for a better explaination.
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Hey guys,
Thanx for all the help. It appeared that the 'find' portion of the HM Help was not installed properly. But I found the explanation now and gained more info from you guys.
Thanx again.
Adios
G
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