Mechanics Based Design of Structures and Machines,
Journal Year:
2024,
Volume and Issue:
unknown, P. 1 - 24
Published: July 23, 2024
This
paper
presents
a
three-dimensional
(3D)
analysis
of
the
post-buckling
behavior
functionally
graded
(FG)
plates
for
first
time
using
an
elastoplasticity-based
meshfree
formulation.
A
novel
3D
Tchebychev-radial
point
interpolation
approach,
which
combines
radial
basis
functions
with
Tchebychev
polynomials,
is
developed
to
solve
nonlinear
problem.
The
incremental
plastic
deformation
modeled
by
Prandtl–Reuss
flow
rule
along
isotropic
hardening
von
Mises
criterion.
governing
equations
are
derived
principle
virtual
work
considering
full
Green–Lagrange
strain
components.
Newton–Raphson
technique
arc-length
method
used
determine
equilibrium
paths
FG
plates.
effective
elastoplastic
properties
material
assessed
exploiting
homogenization
method,
named
Tamura–Tomota–Ozawa
(TTO)
model.
It
has
been
demonstrated
that
accuracy
solution
improved
incorporating
polynomials
into
(RPIM)
shape
function,
and
stability
robustness
results
independent
variations
in
parameter.
Furthermore,
it
confirmed
TRPIM,
slightly
higher
CPU
compared
RPIM,
exhibits
convergence
rate.
excellent
agreement
those
existing
literature
shows
proposed
can
be
as
robust
accurate
numerical
tool
predict
Further
assessments
indicate
significantly
affected
factors
such
geometric
parameters,
gradient,
loading
ratio,
boundary
conditions
(BCs).
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik,
Journal Year:
2023,
Volume and Issue:
104(2)
Published: Nov. 20, 2023
Abstract
The
large‐amplitude
vibration
of
initially
stressed
functionally
graded
material
(FGM)
rectangular
plates
with
porosities
is
investigated
in
this
paper.
All
edges
the
plate
are
simply
supported
and
uncompressed
tangentially
restrained.
Initial
stresses
caused
by
in‐plane
compressive
load
acting
on
freely
movable
or
thermally
induced
forces
at
restrained
edges.
Pores
present
FGM
through
even
uneven
distributions.
Material
properties
assumed
to
be
temperature‐dependent
and,
due
presence
pores,
effective
determined
using
a
modified
rule
mixture.
Governing
equations
terms
deflection
stress
function
established
based
classical
theory
taking
into
account
von
Kármán
nonlinearity
initial
geometric
imperfection.
These
solved
approximate
analytical
solutions
along
Galerkin
method
obtain
time
differential
equation
containing
quadratic
cubic
nonlinear
terms.
Nonlinear
frequencies
means
numerical
integration
employing
fourth‐order
Runge–Kutta
scheme.
Parametric
studies
carried
out
analyze
effects
geometry
properties,
porosity
volume
fraction
distribution,
pre‐existent
thermal
loads,
imperfection
degree
tangential
constraints
unloaded
natural
linear
frequency
ratio
plates.
