A novel hybrid 8-node plate element for capturing the nonlocal effect based on the Hellinger-Reissner variational principle
Abstract
The
Hellinger-Reissner
variational
principle
based
hybrid
finite
element
method
(FEM)
is
developed
and
applied
to
study
the
nonlocal
mechanics
of
plates
beams
at
a
micro/nano-scale.
For
this
purpose,
plane
8-node
plate
termed
as
MHAS-24β
with
24
independent
internal
force
parameters
proposed
modelling
mechanical
behaviors
including
static
bending,
free
vibration
buckling.
Mindlin
theory
allows
use
generalized
displacement
satisfy
\({\text{C}}^{\text{0}}\)
continuity
requirements,
making
it
applicable
different
thicknesses.
To
overcome
shear
locking,
assumed
strain
(ASM)
adopted
modify
original
strains.
polynomials
for
forces
are
be
related
highest-order
derivatives
variables,
them
complete
capable
avoiding
zero-energy
mode.
posterior
error
estimation
indicates
that
convergence
order
not
affected
by
parameter,
thickness
or
shape.
effectively
captures
effect
outperforms
displacement-type
FEM
low-order
described
in
previous
literature.
Research Square (Research Square), Journal Year: 2024, Volume and Issue: unknown
Published: May 29, 2024
Language: Английский