18 A Plausible Description of Continuum …
369
Fig. 18.54 Hexagonal lattice reduced neighbor numbers
the ratio length/width up to 10 or more. Although the external shape of the beam can
sometimes be acceptable, once again we can see as the displacement of the internal
particles is quite different from the FEM solutions; it is clear that the differences are
sometimes noticeable, as outlined by the von Mises’ graphs. So far we stop trial and
errors to think about a better understanding of the physic behind the tool and what
should drive our choices in the tool to describe material continuum. This will be the
object of the next paper.
18.5 Future Work
The presented results are interesting, but they still are at a preliminary stage. We have
collected some success showing plausible deformation in different conditions but
when we consider a beam under loading, the need to connect constitutive equations
with the parameters of our tool emerges powerfully. We have stressed what still need
to investigate as a beam under shear stress. Changing the parameters of our tool, we
obtain different results nobody of them perfectly coincident with classical solution.
The reason of this lies in the fact that, up to now, we do not start from the constitutive
equations of the materials to obtain the rules governing points displacement. So far
the most important topic to be investigated is concerning how to relate materials
parameters with the choices we are doing in our tool. This must be done to achieve
a connection with the usual methods of continuum mechanics. As matter of fact,
we, actually, have not criteria about how direct our tool’s choices to describe a
particular material continuum. In the beam deformation, we have assigned Young’s
modulus and Poisson’s coefficient, but there is no relationship between them and
the parameters of our model, i.e., the follower’s rules. This is the reason of the
discrepancy in the resulting deformation compared to FEM solution.
Generalization in 3D of the tool is quite easy but still needs some optimization in
the code to keep the computation time in the order of seconds, by using a normal PC
desktop.
369
Fig. 18.54 Hexagonal lattice reduced neighbor numbers
the ratio length/width up to 10 or more. Although the external shape of the beam can
sometimes be acceptable, once again we can see as the displacement of the internal
particles is quite different from the FEM solutions; it is clear that the differences are
sometimes noticeable, as outlined by the von Mises’ graphs. So far we stop trial and
errors to think about a better understanding of the physic behind the tool and what
should drive our choices in the tool to describe material continuum. This will be the
object of the next paper.
18.5 Future Work
The presented results are interesting, but they still are at a preliminary stage. We have
collected some success showing plausible deformation in different conditions but
when we consider a beam under loading, the need to connect constitutive equations
with the parameters of our tool emerges powerfully. We have stressed what still need
to investigate as a beam under shear stress. Changing the parameters of our tool, we
obtain different results nobody of them perfectly coincident with classical solution.
The reason of this lies in the fact that, up to now, we do not start from the constitutive
equations of the materials to obtain the rules governing points displacement. So far
the most important topic to be investigated is concerning how to relate materials
parameters with the choices we are doing in our tool. This must be done to achieve
a connection with the usual methods of continuum mechanics. As matter of fact,
we, actually, have not criteria about how direct our tool’s choices to describe a
particular material continuum. In the beam deformation, we have assigned Young’s
modulus and Poisson’s coefficient, but there is no relationship between them and
the parameters of our model, i.e., the follower’s rules. This is the reason of the
discrepancy in the resulting deformation compared to FEM solution.
Generalization in 3D of the tool is quite easy but still needs some optimization in
the code to keep the computation time in the order of seconds, by using a normal PC
desktop.