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Jacobian matrix in ABAQUS UEL

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Chen Li

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Jul 16, 1999, 3:00:00 AM7/16/99
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I am writing a User Element of ABAQUS, when interface with ABAQUS,
the software ask me to define 'residual vector' in one matrix and
'jacobian matrix' in another.

But what is the jacobian matrix of an element?


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Daniel Thuresson

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Jul 16, 1999, 3:00:00 AM7/16/99
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Chen Li wrote:

Hi Chen Li,

The Jacobian matrix (J) for an element is used for isoparametric
formulation of an element, and controls the mapping between the
"iso-domain" and the real geometry. It is defined as follows (for a
plane four node element):

J=[Dn]*[x0 y0]

where Dn=[dN/deta dN/dxi]
x0 and y0 are the coordinate vectors of the nodes.
dN/deta and dN/dxi are the shape function derivatives with respect to
eta and xi respectively. eta and xi are the isoparametric coordinates.
I'm not sure if this will help you since I've never used Abaqus myself
and don't know what information the program wants. But hopefully you
will have some use of it. If not I can recommend a book which explains
your problem:
"Concepts and Applications of Finite Element Analysis" by Robert D. Cook
etc.ISBN 0-471-50319-3

best wishes,
/Daniel


Eric Cabrol

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Jul 19, 1999, 3:00:00 AM7/19/99
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Daniel Thuresson wrote:
>
> Chen Li wrote:
>
> > I am writing a User Element of ABAQUS, when interface with ABAQUS,
> > the software ask me to define 'residual vector' in one matrix and
> > 'jacobian matrix' in another.
> >
> > But what is the jacobian matrix of an element?
> >
> > Sent via Deja.com http://www.deja.com/
> > Share what you know. Learn what you don't.
>
> Hi Chen Li,
>
> The Jacobian matrix (J) for an element is used for isoparametric
> formulation of an element, and controls the mapping between the
> "iso-domain" and the real geometry. [...]


I agree with this definition, but why would you restrain it to
isoparametric elements ? The sub/iso/super-parametric characteristic of
an element only indicates that the polynomial interpolation used for the
displacement field is resp. lower/equal/greater than the one used for
the shape functions ...

Eric

Daniel Thuresson

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Jul 30, 1999, 3:00:00 AM7/30/99
to Eric Cabrol
Hi Eric,

I didn't know of such a distinction. I thought the elements were called
"Isoparametric elements" regardless of the polynomial interpolation. But
thanks for enlightening me.

/Daniel

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