Authors :
Adamu Musa Mohammed; Abdulrahman A. Abdulrasheed; Usman Dadum Hamza
Volume/Issue :
Volume 8 - 2023, Issue 5 - May
Google Scholar :
https://bit.ly/3TmGbDi
Scribd :
https://t.ly/1FMMy
DOI :
https://doi.org/10.5281/zenodo.8042289
Abstract :
Mathematical models, which have already
become essential tools in modern engineering, can be
used to forecast and simulate the multi physical
behaviour of various engineering systems and problems,
whether in their simpler or complex forms. In this work,
a linear elasticity problem involving a rectangular
geometry of a wooden bar with an imposed load at one
end and fixed at the other end was simultaneously solved
by mesh and mesh-free particle methods. Elmer, a finite
element program, was utilized for the mesh-based
method, whereas Lattice Spring Model was used for the
particle method. In the mesh-based technique, a
Poisson's ratio of 0.37 was typically used.
Comparatively, the Poisson's ratio for a lattice spring
was discovered to always be 0.25 when using the particle
technique, which is consistent with earlier findings in the
literature. A numerical comparison of the data reveals
that, despite the two methods' differing Poisson's ratios,
they provide results that are very similar. In fact, the
resulting stresses are only partially dependent on the
Poisson’s ratio. When, in the mesh-based method, the
Poisson ratio is changed to 0.25, the values for the
maximum stress are only slightly lower than those for
0.37.
Keywords :
Mesh; Mesh-free; Modeling; Elasticity; Young Modulus; Poisson’s ratio; Elmer; LSM; LAMMPS. Particlebased modelling technique
Mathematical models, which have already
become essential tools in modern engineering, can be
used to forecast and simulate the multi physical
behaviour of various engineering systems and problems,
whether in their simpler or complex forms. In this work,
a linear elasticity problem involving a rectangular
geometry of a wooden bar with an imposed load at one
end and fixed at the other end was simultaneously solved
by mesh and mesh-free particle methods. Elmer, a finite
element program, was utilized for the mesh-based
method, whereas Lattice Spring Model was used for the
particle method. In the mesh-based technique, a
Poisson's ratio of 0.37 was typically used.
Comparatively, the Poisson's ratio for a lattice spring
was discovered to always be 0.25 when using the particle
technique, which is consistent with earlier findings in the
literature. A numerical comparison of the data reveals
that, despite the two methods' differing Poisson's ratios,
they provide results that are very similar. In fact, the
resulting stresses are only partially dependent on the
Poisson’s ratio. When, in the mesh-based method, the
Poisson ratio is changed to 0.25, the values for the
maximum stress are only slightly lower than those for
0.37.
Keywords :
Mesh; Mesh-free; Modeling; Elasticity; Young Modulus; Poisson’s ratio; Elmer; LSM; LAMMPS. Particlebased modelling technique
