On Sun, 5 May 2002, will kim wrote:

> It seems well known that if a model contains  many degenerated 4-node
> elements, its results from the explicit algorithm will be less
> reliable. Can anyone here provide a brief theoretical explanation
> about the effect of degenerated 4-node element on FE calculation
> results in the explicit algorithm.

Avoiding your question (sorry), if you identify the 2 co-incident nodes,
you can under many, if not most circumstances, use a routine ( if it is
available ) which has formulated the algebra in terms of 3 nodes, not 4.
While this does not consider the case where the 2 nodes not co-incident
but simply very close to each other, this eliminates those numerical
problems for the purely co-incident case. In most isoparametric shells,
the algebra is a function of the number of nodes.  Integration rules for a
triangle are very different to those of a quadrilateral.

Mind you, if you are stuck with somebody's package that has no triangles,
you are a bit out of luck.

The same applies for degenerated bricks but only where you have a 1 or 3
fully collapsed faces, i.e. it is a pentahedron or tetrahedron.  A single
collapsed edge is not sufficient to create a simple geometric shape which
has an easily know algebraic solution. This case is so bad I would not
begin to know where to start.  With so many different combinations, this
3D case would be 100 times more complicated to implement than the 2D case.

- Damian

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