From: "Tom Krajci" 
To: 
Reply-To: "Tom Krajci" 


>From: Aplanatic{at}aol.com

>Support a primary mirror from its center only, as on a baffle tube for
a >Cassegrain.  Grind a conical shape into the back of the mirror so
that the >edge of the mirror is thinner than the center.  Under gravity,
what is the >RMS error in the mirror's surface given a cross-sectional
profile for the >mirror?  Assume that 2nd order deflection is removed by
re-focusing.....

>What is the best shape for the back of the mirror to minimize the RMS
>error?  How large and thin (light-weight) can we make the mirror with
this
>support?  Is there a better shape for the back of the mirror than
>conical?...

>Is there a finite element analysis program available on the web that
can >handle this geometry?  When gravity is normal to the mirror, the
problem >reduces to one dimension.  It should be a fairly simple
analysis for this >case.  Any FEA experts out there?

I'm certainly no expert on this.  However, maybe GRAPE software is a good
starting point?  It can handle up to 4096 nodes and 4096 elements. It can
take into account the mass of the truss under acceleration of gravity, etc.
See:
http://overton.tamu.edu/aset/krajci/
and especially pages on flexure analysis of various components, and:
http://overton.tamu.edu/aset/krajci/truss-analysis/truss-analysis.htm
lists the location of GRAPE:
http://www.grapesoftware.mb.ca/
and Felt:
http://felt.sourceforge.net/

I have no experience with FElt.  With GRAPE I can help you build a truss
arrangement to analyze this case.  I'm learning how to build the nodes and
elements pretty well with some of its features.

Also see some work by Tony Owens at:
http://overton.tamu.edu/aset/krajci/cell-bearing.htm
(see section on compliant hinges...two designs by Tony.  One of them is a
central hole/support, but with a whiffletree in the back, and a
disk/constant thickness mirror)

Hope this helps,
Tom Krajci
Tashkent, Uzbekistan


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