Re: leaf spring energy

[David Dockstader <DRDOCK00@UKCC.UKY.EDU>]

On Sun, 19 Apr 1998 12:17:14 -0700 (PDT) James Mclean said:
> Please elaborate on the ellipsoid visualization.  I'm not seeing how
> rotating a diagonal matrix can be so represented.  Do you mean a genuine
> ellipsoid, or just an oval-oid like shape?
The stress ellipse/ellipsoid represents only normal stress.  I should have made
this clear from the start.  The axes of the ellipse/ellipsoid give magnitude
and direction of the principal stresses.

Now back to the bending beam.  The usual formulation is for a buckling beam.
The boundary conditions on the ends are that the only stress is a compressive
stress.  These boundary conditions create nice freindly solvable equations.
Your boundary conditions (for the bending leaf spring) are different, so
naturally your stresses will be different.  Thus, at least near the ends, your
max shear stresses are not on a plane +/- 45 deg to surface, but closer to 90.
My "intuition" tells me this is a much harder problem to solve.  Again, my
intuition tells me that the problem of pure shear and small phi is doable and
probably what you will find in the aircraft reference cited.  What would be
interesting is to see the inbetween cases with a mix of normal stress and
shear on the ends and then let phi grow.  I think Pro Engineer can do this.
I'm up to my neck with end of semester woes right now, but in a week or two
I should be able to sit down with my son and get him to run it.  I'll let you
know if it works.  I've never used the program or even seen it run.  I just
know what he tell me about it.  He was so impressed he bought stock in the
company.