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The
geometric non-linear shell elements
which are currently available
in XFINAS is based on the Updated
Lagrangian method. The formulation
of these elements uses Mindlin-Reissner
theory, which the formulation
of the linear and geometrical
stiffness is exactly defined
by incorporating membrane forces,
bending moment and transverse
shear resultant force. In order
to remove rigid body rotations,
the co-rotational method is
used. The material is assumed
to be isotropic, laminated composite
and elasto-plastic material.
Plasticity is handled by applying
the von Mises yield condition
and Prandl-Reuss flow rule to
discrete points through the
shell wall. By using six degrees
of freedom per node, the present
element can model stiffened
plate and shell structures.
The
transverse shear stiffness in
the laminated composite materials
is defined by an equilibrium
approach instead of using the
shear correction factor. Four
macroscopic progressive failure
criteria for fiber-reinforced
composite under loading were
implemented. These criteria
may be used to check for first
ply failure of composite structures
or in determining ultimate loads
for complete laminate failure
and getting risk assessment.
An
assumed strain quasi-conforming
shell element
A
new Quasi-conforming formulations
of 4-node stress resultant shell
element ( XSHELL41 ) is developed
and implemented in the XFINAS
for the solution of stability
problems of stiffened plates
and shells. The shear-locking
behaviour is eliminated by using
the Quasi-conforming method.
The stiffness matrices for the
present elements are explicitly
expressed and the stresses are
taken accurately at the nodal
points. Compared to elements
using Gauss integration, where
the stresses are most accurate
at the integration points, the
extrapolation procedure needed
for post processing is eliminated
in the present shell element.
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