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ANSYS shell elements
Contact: b.banerjee.nz@gmail.com 2011-July-13
response of the SOLSH190 element is between 6%-8% less stiff than suggested by Mindlin theory.
Part b shows that the SOLSH190 element is, in general, stiffer than the SHELL181 element. If
three elements are used through the thickness, the response is stiffer than when one element is
used.
Parts c and d of the figure show the bending stress solutions. The bending stresses are higher
than those predicted by Mindlin theory. Both SOLSH190 and SHELL181 elements predict nearly
identical bending stresses. The errors at the boundary of the plate are lower when three elements
are used through the thickness but higher at the center of the plate.
The mid-surface transverse shear stresses are shown in parts e and f of the figure. In this case
the SHELL181 and three-element SOLSH190 results are quite close but differ significantly from
Mindlin theory at the edges of the plate. There are slight differences between the other SOLSH190
solutions, but all options lead to values that are close to Mindlin theory at the boundaries and the
center of the plate.
2.4 The SOLID185 element
The SOLID185 element is also a linear element with three translational degrees of freedom at each
of its 8 nodes. This element is convenient for checking the performance of shell and solid shell
elements for situations where exact solutions are not available. Simulations have shown that three
elements through the thickness are adequate for modeling isotropic plates. Most of the results
discussed in this section use three SOLID185 elements through the thickness of the plate. Stresses
and displacements predicted by SOLID185 elements are compared with SHELL181 simulations
(with KEYOPT(3) = 0, 3 integration points through-thickness, 80 elements along an edge) and
SOLSH190 simulations (1 layer, 3 through-thickness integration points, 80 elements along edge).
Displacements and stresses for the simply supported thin plate under uniform pressure load are
shown in Figure 6 (p. 14). The SOLID185 results include a mesh refinement study (n = 40, n = 80,
n = 160) with KEYOPT(2) = 2 which is an enhanced strain formulation. The n = 80 case is also
compared with the situation where KEYOPT(2)=0 when a full
¯
B integration is used. The effect
of the number of elements though the thickness is examined by changing the number of elements
through-thickness from 3 to 5 (e = 5).
Part a of the figure shows that when the full integration is used, the response of the plate is
significant less stiff than that predicted by Kirchhoff-Love plate theory. The difference between the
“exact” solution and the ANSYS
TM
results shown in part b indicates that the SOLID185 solution
converges to the SOLSH190 solution with increasing mesh refinement. SHELL181 elements give a
larger absolute displacement.
If we examine the bending stress solutions in parts c and d of the figure, we once again see that
fully integrated SOLID185 elements underestimate the stress significantly. However, the difference
between SOLID185, SOLSH190, and SHELL181 elements is marginal as far as the bending stress
is concerned. Large errors are again observed at the edges of the plate because of a flattening of the
stress distribution. This may only be an artifact of the interpolation process used by ANSYS
TM
to
populate nodal stress data.
The mid-surface transverse shear stress results shown in parts e and f of the figure indicate that
¯
B and enhanced strain methods give nearly identical results that differ from Kirchhoff-Love theory
at the edges of the plate. However, the SOLSH190 and SOLID185 results are quite different with
the SOLSH190 simulations giving results closest to the exact solution.
For the thick plate, the effect of mesh refinement and integration points (through the thickness)
on the ANSYS
TM
solution is shown in Figure 7 (p. 15). The results are similar to those for a thin
plate except that an increase in the number of elements through-thickness (e = 5) gives a less stiff
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