Two Dimensional Formulation Elasticity Lifeng Wang Body Forces Assume Body For

1) The beam -b < y <b, 0 < x < L is built-in at the edge x = L and is loaded merely by its own weight, pg per unit volume. Find a solution for the stress field, using weak conditions on the end x = 0.
p is in place of rho for density.
2) A large plate with a small central hole of radius a is subjected to in-plane hydrostatic compression (sigma)_xx=(sigma)_yy=-S, (sigma)_xy=0 at the remote boundaries.  Find the stress field in the plate if the surface of the hole is traction-free.
3)  The figure (last slide of attached file) shows a thin uniform circular disk, which rotates at constant speed (omega) about the diametral axis y= 0, all the surfaces being traction-free.  Determine the complete stress field in the disk.
  All problems are from Elasticity by JR barber.
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