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

[+] Author and Article Information
Ashok V. Kumar, Jongho Lee

Department of Mechanical and Aerospace Engineering,  University of Florida, Gainesville, FL 32611

J. Mech. Des 128(1), 46-56 (Apr 13, 2005) (11 pages) doi:10.1115/1.2121743 History: Received June 23, 2004; Revised March 03, 2005; Accepted April 13, 2005

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.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Quadratic nine-node element in two different coordinate systems

Grahic Jump Location
Figure 2

Density distribution within a nine-node quadrilateral element

Grahic Jump Location
Figure 3

Node numbering for 8-node and 18-node hexahedral element

Grahic Jump Location
Figure 4

Solid primitive created by extruding ellipse

Grahic Jump Location
Figure 5

Mapping from cylindrical to cartesian coordinates

Grahic Jump Location
Figure 6

Solid primitive created by revolving a circle

Grahic Jump Location
Figure 7

Sweep trajectory and coordinate systems used for a sweep element

Grahic Jump Location
Figure 8

Primitive created by sweeping a circle along a parametric curve

Grahic Jump Location
Figure 9

Constructive solid geometry tree

Grahic Jump Location
Figure 15

Normal stress computed using nonconforming grid

Grahic Jump Location
Figure 10

CSG tree of solids created using step functions

Grahic Jump Location
Figure 11

Comparison between ordinary and regularized Boolean operations

Grahic Jump Location
Figure 12

Approximation errors in Boolean result

Grahic Jump Location
Figure 13

Analysis using nonconforming mesh

Grahic Jump Location
Figure 14

Plate with mesh and boundary condition




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In