...
What
...
is
...
the
...
difference
...
between
...
thin
...
and
...
thick
...
shell
...
formulations?
...
Answer:
...
The
...
inclusion
...
of
...
transverse
...
shear
...
deformation
...
in
...
plate-bending
...
behavior
...
is
...
the
...
main
...
difference
...
between
...
thin
...
and
...
thick
...
...
formulation.
...
Thin-plate
...
formulation
...
follows
...
a
...
Kirchhoff
...
application,
...
which
...
neglects
...
transverse
...
shear
...
deformation,
...
whereas
...
thick-plate
...
formulation
...
follows
...
Mindlin/Reissner,
...
which
...
does
...
account
...
for
...
shear
...
behavior.
...
Thick-plate
...
formulation
...
has
...
no
...
effect
...
upon
...
membrane
...
(in-plane)
...
behavior,
...
only
...
plate-bending
...
(out-of-plane)
...
behavior.
...
Shear
...
deformation
...
tends
...
to
...
be
...
important
...
when
...
shell
...
thickness
...
is
...
greater
...
than
...
approximately
...
1/
...
5 to
...
1/
...
10 of
...
the
...
span
...
of
...
plate-bending
...
curvature.
...
Shearing
...
may
...
also
...
become
...
significant
...
in
...
locations
...
of
...
bending-stress
...
concentrations,
...
which
...
occur
...
near
...
sudden
...
changes
...
in
...
thickness
...
or
...
support
...
conditions,
...
and
...
near
...
openings
...
or
...
re-entrant
...
corners.
...
Thick-plate
...
formulation
...
is
...
best
...
for
...
such
...
applications.
...
Thick-plate
...
formulation
...
is
...
also
...
recommended
...
in
...
general
...
because
...
it
...
tends
...
to
...
be
...
more
...
accurate,
...
though
...
slightly
...
stiffer,
...
even
...
for
...
thin-plate
...
bending
...
problems
...
in
...
which
...
shear
...
deformation
...
is
...
truly
...
negligible.
...
However,
...
the
...
accuracy
...
of
...
thick-plate
...
formulation
...
is
...
sensitive
...
to
...
...
distortion
...
and
...
large
...
aspect
...
ratios,
...
and
...
therefore
...
should
...
not
...
be
...
used
...
in
...
such
...
cases
...
when
...
shear
...
deformation
...
is
...
known
...
to
...
be
...
small.
...
In
...
general,
...
the
...
contribution
...
of
...
shear
...
deformation
...
becomes
...
significant
...
when
...
ratio
...
between
...
the
...
span
...
of
...
plate-bending
...
curvature
...
and
...
thickness
...
is
...
approximately
...
20:1
...
or
...
10:1.
...
The
...
formulation
...
itself
...
is
...
adequate
...
for
...
ratio
...
down
...
to
...
5:1
...
or
...
4:1.
...
In
...
that
...
this
...
ratio
...
is
...
dependent
...
upon
...
the
...
projected
...
span
...
of
...
curvature,
...
shell
...
thickness
...
may
...
be
...
greater
...
than
...
the
...
actual
...
plan
...
dimensions
...
of
...
a
...
shell
...
object.
...
Stiffness for pure-bending
...
deformation
...
The
...
statement
...
that
...
thick
...
shells
...
tend
...
to
...
be
...
stiffer
...
than
...
thin
...
shells
...
applies
...
only
...
to
...
the
...
bending
...
components
...
of
...
shells,
...
and
...
to
...
models
...
in
...
which
...
...
is
...
too
...
coarse.
...
When
...
meshing
...
adequately
...
captures
...
bending
...
deformation,
...
thick-shell
...
elements
...
are
...
more
...
flexible
...
because
...
of
...
the
...
additional
...
shear
...
deformation
...
that
...
is
...
not
...
captured
...
through
...
thin-shell
...
formulation.
...
Given
...
pure-bending
...
deformation,
...
however,
...
the
...
thin-shell
...
element
...
is
...
slightly
...
more
...
accurate,
...
therefore
...
the
...
thick-shell
...
element
...
may
...
be
...
stiffer
...
for
...
coarser
...
meshes.
...
This
...
effect
...
diminishes
...
as
...
the
...
mesh
...
is
...
refined.
...
Stresses
...
may
...
be
...
of
...
greater
...
concern
...
than
...
deflections.
...
When
...
shear
...
deformation
...
is
...
expected
...
to
...
be
...
important,
...
we
...
recommend
...
the
...
thick-shell
...
element
...
because
...
it
...
will
...
better
...
capture
...
the
...
stress
...
distribution.
...
This
...
is
...
the
...
case
...
not
...
only
...
for
...
thicker
...
shells,
...
but
...
also
...
for
...
regions
...
near
...
openings
...
and
...
other
...
geometric
...
discontinuities
...
in
...
which
...
transverse
...
shear
...
deformation
...
develops
...
.
...