Step Function Representation of Solid Models and Application to Mesh Free Engineering Analysis

Abstract

Numerical methods for solving boundary value problems that do not require generation of mesh to approximate the analysis domain have been referred to as mesh-free methods. While many of these are “mesh less” methods that do not have connectivity between nodes, a subset of these methods uses a structured mesh or grid for the analysis that does not conform to the geometry of the domain of analysis. Instead the geometry is represented using implicit equations. In this paper we present a method for constructing step functions of solids whose boundaries are represented using implicit equations. Step functions can be used to compute volume integrals over the solid that are needed for mesh free analysis. The step function of the solid has a unit value within the solid and zero outside. A level set of this step function can then be defined as the boundary of the solid. Boolean operators are defined in this paper that enable step functions of half-spaces and primitives to be combined to construct a single step function for more complex solids. Application of step functions to analysis using nonconforming mesh is illustrated.