Biomedical Engineering Reference
In-Depth Information
Additionally, the software permits to analyse the problem considering the three-
dimensional deformation theory, the plane stress and the plane strain two-
dimensional deformation theory, several plate shear deformation theories, such as
the Reissner-Mindlin deformation theory, the third-order shear deformation theory
and the unconstrained third-order shear deformation theory. The developed
meshless software is being continuously improved with new application fields and
analysis options.
The program allows the user to choose the material disposition along the solid
domain, as well as the principal material orientation for the case of an anisotropic
analysis. The program reads external mesh files generated in the CAD softwares.
Nonetheless it also possesses an algorithm which permits the user to create the
nodal distribution discretizing the problem domain without using the external CAD
softwares. In order to visualize the obtained results the program produces data files
which can be open in external CAD softwares, permitting to explicitly analyse and
understand the deformation field and the stress distribution along the solid domain.
Besides the pre-processing phase and the pos-processing phase, the global NNR-
PIM analysis program is independent from any other external software. All the
examples shown in this topic were analysed using the author's meshless software.
1.6 Book Arrangement
This topic is divided in seven chapters. In the first chapter it is introduced the topic
purpose. A general overview on the meshless method state of the art is shown and the
used meshless method is briefly presented. Regarding the bone tissue remodelling
numerical analysis topic, the most relevant research works are also mentioned.
In the second chapter the solid mechanics fundamentals are briefly presented.
The continuum formulation is presented, along with the used weak formulation
and the discrete system equations obtained for the elastostatic and elastodynamic
solid mechanical problem.
The meshless method procedure is fully presented in the third chapter. The
main differences and similarities between the meshless methods and the FEM are
shown and explained. The enforcement of the nodal connectivity in meshless
methods is described in detail, along with the introduction of meshless concepts,
such as ''influence-domains'' and the ''influence-cells''. Additionally, numerical
tools to construct background integration meshes are presented. The presented
integration schemes permit to obtain nodal dependent and nodal independent
background integration meshes. In the end of the chapter the numerical imple-
mentation using meshless methods is fully addressed.
The fourth chapter shows how to construct shape functions for meshless
methods. The ''support-domain'' concept is firstly presented. Then, two of the
most popular shape functions used in meshless methods are presented in detail:
approximation
functions
constructed
using
the
moving
least
square
(MLS)
approximation
and
interpolation
functions
obtained
with
the
radial
point
