Biomedical Engineering Reference
In-Depth Information
Meshless method gradually begin to enter the bone remodelling application
field [
90
]. Liew and co-workers [
91
] presented one of the first works dealing with
bone structures and using meshless methods. A simple stress analysis of a femoral
bone model was performed and some meshless methods limitations are identified.
All the meshless limitations indicated [
91
] do not represent a difficulty for the
NNRPIM, which can easily deal with the non-convex boundaries and the material
discontinuities in the bone structure. Other authors applied the meshless methods
to the bone tissue analysis [
92
,
93
] and more recently Belinha and co-workers
[
94
,
95
] presented a new bone tissue remodelling algorithm relying on the
meshless method accuracy.
1.4 Book Purpose
The present topic results from the author's MSc and PhD monographs [
96
,
97
] and
from the support texts of the unit course: ''Meshless Methods: A Introduction
Course'' directed and lectured by the author. Therefore, the main purpose of this
work is to provide an explanatory academic text book on meshless methods (with a
particular emphasis on the NNRPIM), which can be used and understood by
university students and researchers interested in meshless methods for computa-
tional mechanics.
Regarding the bone tissue remodelling analysis, in this topic a gradient remod-
elling algorithm is used, in which the bone tissue anisotropic material properties
gradually vary through the model domain, in accordance with the proposed phe-
nomenological anisotropic material law and the lower SED regions [
94
,
95
].
Thus, the present work expects to contribute with new efficient numerical tools
and strategies, such is the use of the proposed bone tissue gradient remodelling
algorithm combined with the NNRPIM, in order to improve the trabecular bone
tissue remodelling analysis field.
1.5 Meshless Method Software
During the last 10 years the author developed an original meshless code, con-
taining more than 50.000 code lines, written in FORTRAN. The meshless code
permits to analyse several solid mechanical problems using the EFGM, the RPIM,
the NNRPIM, the NREM and the FEM (for comparison purposes).
The code is capable of solving various engineering problems, such as:
• Static and dynamic linear problems;
• Nonlinear large deformation static problems;
• Elasto-plastic static problems;
• Structural topology optimization problems;
• Crack opening path problems;
