Civil Engineering Reference
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to allow for the shell thickness in finite-strain elements to change as a func-
tion of the membrane strain. If the section Poisson's ratio is defined as zero,
the shell thickness will remain constant and the elements are, therefore,
suited for small-strain, large-rotation analysis. The change in thickness is
ignored for the small-strain shell elements in ABAQUS [1.29].
Conventional reduced-integration shell elements can be also classified
based on the number of degrees of freedom per node. Hence, there are two
types of conventional reduced-integration shell elements known as
five-
degree-of-freedom and six-degree-of-freedom shells
. Five-degree-of-freedom
conventional shells have 5 degrees of freedom per node, which are three
translational displacement components and two in-plane rotation compo-
nents. On the other hand, six-degree-of-freedom shells have 6 degrees of
freedom per node (three translational displacement components and three
rotation components). The number of degrees of freedom per node is
commonly denoted in the shell name by adding digit 5 or 6 at the end
of the reduced-integration shell element name. Therefore, reduced-
integration shell elements S4R5 and S4R6 have 5 and 6 degrees of freedom
per node, respectively. The elements that use 5 degrees of freedom per
node such as S4R5 and S8R5 can be more economical. However, they
are suitable only for thin shells and they cannot be used for thick shells.
The elements that use 5 degrees of freedom per node cannot be used
for finite-strain applications, although they model large rotations with
small strains accurately.
There are a number of issues that must be considered when using shell
elements. Both S3 and S3R refer to the same three-node triangular shell ele-
ment. This element is a degenerated version of S4R that is fully compatible
with S4 and S4R elements. S3 and S3R provide accurate results in most
loading situations. However, because of their constant bending and mem-
brane strain approximations, high mesh refinement may be required to cap-
ture pure bending deformations or solutions to problems involving high
strain gradients. Curved elements such as S8R5 shell elements are preferable
for modeling bending of a thin curved shell. Element type S8R5 may give
inaccurate results for buckling problems of doubly curved shells due to the
fact that the internally defined integration point may not be positioned on
the actual shell surface. Element type S4 is a fully integrated, general-
purpose, finite-membrane-strain shell element. Element type S4 has four
integration locations per element compared with one integration location
for S4R, which makes the element computation more expensive. S4 is com-
patible with both S4R and S3R. S4 can be used in areas where greater
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