ABSTRACT
Previous chapters have described the detailed formulation and procedures of MFree methods; this chapter focuses on issues related to code implementation of MFree methods. Naturally, different MFree methods contend with different issues related to coding implementation. Here we discuss only those issues that are common to most MFree methods:
• Definition of the support domain or influence domain • Need for a background mesh for integration • Node searching • Dealing with domains of complex and irregular boundaries • Error estimation • Adaptive algorithm
In previous chapters, we used the concept of a support domain for a point of interest (usually the quadrature point
x
or the center of the integration cell) in the problem domain, as shown in Figure 4.2. The function of the support domain is basically to determine the field nodes used for constructing shape functions. It is used not only in the process of establishing system equations, but also in the process of retrieving solutions for field variables at locations other than the nodes or derivatives of the field variables at any point in the problem domain. Using the concept of support domain, we simply say that all the nodes that fall into the support domain of a point will be used for constructing shape functions. This works well, if the nodal density does not vary too drastically in the problem domain, but often fails for domains with drastic nodal density variations, such as problems with stress singularity, where the nodal density can vary drastically. For this kind of problem, we suggested the use of the concept of influence domain (see Figure 2.9) to select nodes for construction of shape functions. MFree2D
, which is the focus of the next chapter, uses this approach to select nodes for constructing shape functions. The difference between the support domain and the influence domain is that the support domain is defined for the quadrature points, and the influence domain is defined for the field nodes.
