Biomedical Engineering Reference
In-Depth Information
Chapter 1
Introduction
Abstract The bioengineering design process can be divided in many specific
phases. The present work lean over three of these phases: the Modulation, the
Simulation and the Analysis. All this process is recurrent by nature, always
looking for the numerical approach which better reproduces the studied phe-
nomenon. At the present time, there are many numerical methods available and
capable to successfully handle the referred bioengineering design process phases.
This work presents, develop and extends a new advance discretization meshless
technique. From the simple solid mechanical problems to the complex nonlinear
bone tissue remodelling analysis in biomechanics, this work shows that the pro-
posed numerical method is flexible and accurate.
1.1 Meshless Methods
In the last few years meshless methods for numerically solving partial differential
equations came into focus of interest, especially in the engineering community. In
the meshless methods [
1
-
3
] the nodes can be arbitrary distributed, once the field
functions are approximated within an influence-domain rather than an element. In
opposition to the no-overlap rule between elements in the Finite Element Method
(FEM) [
4
,
5
], in meshless methods the influence-domains may and must overlap
each other. It is possible to define and classify a numerical method by three
fundamental modules: the field approximation (or interpolation) function, the used
formulation and the integration.
1.1.1 Approximation or Interpolation Functions
There are many approximation (or interpolation) functions available. The most
relevant are the Taylor approximation, the moving least-square approximation, the
