L2 Projection for 6-node triangular elements

[boeger]

Dear *,

I'm trying to project Gauss-point variables to nodes using the L2 projection within a custom 6-noded triangular element together with 7 Gauss points. The results aren't satisfactory, and I realized that FEAP's own 2D-solid-element is doing some non-standard calculations to fill the stiffness matrix for 6 nodes and 7 Gauss points (while the right hand side is set to 1.0). Could anyone give me a hint or a reference within the literature, why this kind of projection technique is necessary for these elements?

Many thanks in advance,

Lukas

[Prof. R.L. Taylor]

For many elements we use a least-squares approach with a diagonal projection matrix.  For triangles this gives zero values at the vertex nodes.  Thus for this element we use a local least squares approach to project to the vertex nodes and interpolate to get the mid-side nodes which avoids the singularity.  These values are then averaged.  It is essentially the method used in

"Convergence of an efficient local least-squares fitting method for bases with
compact support",
with S. Govindjee, J. Strain, T.J. Mitchell, R.L. Taylor,
Computer Methods in Applied Mechanics and Engineering,
(http://dx.doi.org/10.1016/j.cma.2011.11.017)
Vol. 213--216, 84--92, 2012.

[boeger]

Ok perfect, many thanks for the quick and clarifying response!