Civil Engineering Reference
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commonly identified based on the number of element nodes and the inte-
gration type. Hence, a shell element S8 means a stress-displacement shell
having eight nodes with full integration, while a shell element S8R means
a stress-displacement shell having eight nodes with reduced integration. On
the other hand,
continuum shell elements
are general-purpose shells that allow
finite membrane deformation and large rotations and, thus, are suitable for
nonlinear geometric analysis. These elements include the effects of trans-
verse shear deformation and thickness change. Continuum shell elements
employ first-order layer-wise composite theory and estimate through-
thickness section forces from the initial elastic moduli. Unlike conventional
shells, continuum shell elements can be stacked to provide more refined
through-thickness response. Stacking continuum shell elements allows for
a richer transverse shear stress and force prediction. It should be noted that
most metal structures are modeled using conventional shell elements, and
hence, they are detailed in this topic.
General-purpose conventional shell elements allow transverse shear
deformation. They use thick shell theory as the shell thickness increases
and become discrete Kirchhoff thin shell elements as the thickness decreases.
The transverse shear deformation becomes very small as the shell thickness
decreases. Examples of these elements are S3, S3R, S4, and S4R shells.
Thick shells are needed in cases where transverse shear flexibility is impor-
tant and second-order interpolation is desired. When a shell is made of the
same material throughout its thickness, this occurs when the thickness is
more than about 1/15 of a characteristic length on the surface of the shell,
such as the distance between supports. An example of thick elements is S8R.
Thin shells are needed in cases where transverse shear flexibility is negligible
and the Kirchhoff constraint must be satisfied accurately (i.e., the shell nor-
mal remains orthogonal to the shell reference surface). For homogeneous
shells, this occurs when the thickness is less than about 1/15 of a character-
istic length on the surface of the shell, such as the distance between supports.
However, the thickness may be larger than 1/15 of the element length.
Conventional shell elements can also be classified as
finite-strain and small-
strain shell elements
. Element types S3, S3R, S4, and S4R account for finite
membrane strains and arbitrarily large rotations; therefore, they are suitable
for large-strain analysis. On the other hand, small-strain shell elements such
as S8R shell elements are used for not only arbitrarily large rotations but only
small strains. The change in thickness with deformation is ignored in these
elements. For conventional shell elements used in ABAQUS [1.29], we
must specify a section Poisson's ratio as part of the shell section definition
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