A meshfree framework for solder droplet shape prediction

In this paper we present a general Non-Uniform-Rational-B-Spline (NURBS) based framework and a set of example problems for solving solder droplet shape. In the recent years, there has been a growing body of literature in meshfree methods. Much of this research is driven by a need to solve problems such as those occurring in fracture where a change in geometry (due to, for instance, crack extension) has necessitated re-meshing in traditional discretization schemes. Large, iterative, changes in geometry are in general characteristic of other class of problems such as large deformation analysis and optimal design. A problem similar in nature to the optimal design problems is the droplet shape problem, where the equilibrium configuration is determined as that possessing the least potential energy. NURBS curves and higher order entities are among the most sophisticated available at the present time to represent complex geometry. The Bernstein polynomials that serve as the basis function in NURBS can be shown to be a partition of unity representation. Thus, the NURBS representation provides an appropriate framework for the representation of field quantities in a meshfree analysis. Such an analysis scheme will be geometry-based and is therefore a very natural one in problems involving large changes in geometry such as the droplet shape prediction problems since changes in geometry need not be accompanied by remeshing. Here we will describe a general purpose java-based code for carrying out optimal design problems. We will illustrate the code using several example problems for solder droplet shape prediction.