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