On admissible external loadings within the first and second strain gradient elasticity
Mathematics and Mechanics of Solids,
Journal Year:
2025,
Volume and Issue:
unknown
Published: April 21, 2025
Recent
extended
applications
of
higher-order
models
continuum
mechanics
as
strain
gradient
elasticity
and
plasticity
result
in
a
certain
extension
possible
external
loadings.
In
addition
to
known
forces
couples,
we
face
double
hyper-stresses
acting
the
volume
on
surface
an
elastic
solid
body.
Despite
fact
that
such
loadings
force
bi-moment
are
already
structural
mechanics,
still
cannot
say
these
quantities
so
obvious
mechanics.
Here,
discuss
admissible
including
those
volume,
surface,
along
curve,
or
even
at
points.
To
establish
this
possibility,
use
Virtual
Work
Principle
(VWP)
generalized
first
second
elasticity.
The
principle
is
foundation
weak
solutions
boundary-value
problems
under
consideration.
From
mathematical
standpoint,
form
linear
functional
corresponding
energy
space
where
solution
exists.
By
loadings,
mean
for
which
bounded,
i.e.,
work
meaningful
total
finite.
Then,
using
Sobolev’s
imbedding
theorems,
characterize
class
VWP
their
physical
meaning.
Language: Английский
A recursive formula to compute Lagrangian actions corresponding to an Eulerian edge H-force in elastic materials with a sufficiently high grade
Mathematics and Mechanics of Complex Systems,
Journal Year:
2024,
Volume and Issue:
12(4), P. 389 - 410
Published: Dec. 29, 2024
Language: Английский