Implicit Solid Modeling for Mesh Free Analysis

2005 ◽  
Author(s):  
Ashok V. Kumar ◽  
Jongho Lee ◽  
Ravi Burla
Keyword(s):  
Solid Modeling ◽  
Step Function ◽  
Characteristic Functions ◽  
Implicit Representation ◽  
Implicit Equation ◽  
Hexahedral Elements ◽  
Unit Value ◽  
Mesh Free ◽  
Implicit Equations ◽  
Representation Scheme

In traditional solid modeling the boundaries of the solid are represented using parametric equations. Even though the application of implicit equations has also been explored, they have not been widely used. Interest has been rekindled recently due to application of implicit equations to mesh free engineering analysis. In this paper, an implicit representation scheme for solids is presented where the boundaries of primitive solids are defined using implicit equation of surfaces. To ensure that the equations are axis independent, the characteristic functions for the implicit equations are defined by interpolating within hexahedral elements. Primitive solids are defined by sweeping closed 2D profiles. The boundaries of these profiles are defined using implicit equations of curves. Implicit equations can be used for constructing “step function” of the primitives and their Boolean combinations. The step functions of a solid has a unit value inside the solid and zero outside and can be used for computing volume integrals needed for mesh free analysis.

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

2005 ◽  
Vol 128 (1) ◽  
pp. 46-56 ◽  
Author(s):  
Ashok V. Kumar ◽  
Jongho Lee
Keyword(s):  
Step Function ◽  
Single Step ◽  
Engineering Analysis ◽  
Step Functions ◽  
Unit Value ◽  
Mesh Free ◽  
Solid Models ◽  
Implicit Equations ◽  
Mesh Free Methods ◽  
Mesh Less

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.

Solution Structures for Imposing Boundary Conditions in Mesh Free Analysis of Heat Conduction Problems

2005 ◽  
Author(s):  
Linxia Gu ◽  
Ashok V. Kumar
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Step Function ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Structured Grid ◽  
Solution Structures ◽  
Mesh Free ◽  
Implicit Equations ◽  
Mesh Free Method

One of the main advantages of meshless methods is that it eliminates the mesh generation, but it is still necessary to place nodes with controlled spacing variation on the boundary and within the domain. However, due to lack of connectivity between nodes it is more difficult to interpolate the field variables and impose boundary conditions. In this paper, a mesh free method is presented for analysis using a structured grid that does not conform to the geometry of the domain. The geometry of the domain is independent of the structured grid and is represented using implicit equations. The implicit equations of the boundaries can be used to construct solution structures that satisfy boundary conditions exactly even though the nodes of the grid are not on the boundaries of the domain. The solution structures are constructed using the implicit equations of the boundary together with a piece-wise interpolation over the structured grid. The implicit equations are also used to construct step function of solid such that its value is equal to unity inside the solid and zero outside. The step function of the solid is used for volume integrations needed for the analysis. The traditional weak form for Poisson’s equation is modified by using this solution structure to eliminate the surface integration terms. The accuracy and implementation of the present mesh free method is illustrated for two-dimensional heat conduction problems governed by Poisson’s equation. Satisfactory results are obtained when compared with analytical results and results from commercial finite element software.

Boolean Algebra and Analysis Using Approximate Step Functions

2004 ◽  
Author(s):  
Ashok V. Kumar ◽  
Jongho Lee
Keyword(s):  
Boolean Algebra ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Level Set ◽  
Boundary Value ◽  
Step Function ◽  
Step Functions ◽  
Unit Value ◽  
Solid Models ◽  
Implicit Equations

Implicit equations of curves and surfaces have been shown to be useful for constructing solutions for boundary value problems such that the boundary conditions are satisfied exactly. This application has generated interest in constructing solid models where the geometry is represented using implicit equations rather than parametric equations. In this paper we present a method for constructing step functions of solids that have 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. This step function can be used not only to apply boundary conditions but also to compute volume integrals over the solid. Methods for combining step functions of solid primitives using ordinary and regularized Boolean operations to construct step functions of the Boolean result are also presented.

THE RAYCASTING ENGINE AND RAY REPRESENTATIONS: A TECHNICAL SUMMARY

1991 ◽  
Vol 01 (04) ◽  
pp. 347-380 ◽  
Author(s):  
J. L. ELLIS ◽  
G. KEDEM ◽  
T. C. LYERLY ◽  
D. G. THIELMAN ◽  
R. J. MARISA ◽  
...  
Keyword(s):  
Large Family ◽  
Solid Modeling ◽  
Brute Force ◽  
Boolean Combination ◽  
Computing Power ◽  
Mass Property ◽  
Intractable Problems ◽  
Boundary Representations ◽  
Computationally Intensive ◽  
Representation Scheme

Solid modeling is computationally intensive. Thus far its use in industry has been limited mainly to simple parts and simple applications, and this is not likely to change much until 'massive' computing power can be made available at an affordable cost. The RayCasting Engine is one specialized source of 'massive' computing power for solid modeling, and it is but the simplest member of a potentially large family of 'classification computers'. The RayCasting Engine (RCE) is a highly parallel, custom-VLSI computer that classifies grids of parallel lines against solids represented in CSG. The sets of parallel 'in' segments that the RCE produces are called ray representations (ray-reps); they can be thought of as sampled boundary representations. Ray-reps are obviously useful for graphics and mass-property calculation. Less obviously, they are surprisingly versatile if one exploits special properties – for example, boolean combination of solids by interval operations on ray-reps – and the fact that ray-reps are cheap to compute. Overall, the combination of a 'new' representation scheme (ray-reps) and a fast custom processor (the RCE) is changing our approach to solid modeling. We are now seeking 'brute force' solutions to problems, and are finding that some previously intractable problems – for example, spatial sweeping and offsetting – are effectively computable and easy to program. This paper summarizes the genesis and principles of the RCE, some important properties of ray representations, and some exemplary applications of the (ray-rep, RCE) combination.

The Research of Using Step Function to Simulate the Step-Movement of Forklift Machine in Mechanical Engineering Based on ADAMS

2013 ◽  
Vol 644 ◽  
pp. 212-215
Author(s):  
Qun Feng Cui ◽  
Xu Rong Li ◽  
Jian Zhang Wang
Keyword(s):  
Mechanical Engineering ◽  
Solid Modeling ◽  
Step Function ◽  
Step Movement ◽  
Step Functions

the movements of forklift mainly include the forward and backward of body,driving of boom cylinder to stick cylinder, flipping and lifting of stick cylinder to shovel,and the recovery of them after the completion of these actions.The paper puts forward using step function in ADAMS to simulate these movements. First, the solid modeling of a forklift established in ADAMS. And then, the step function was utilized to carry on emulation step by step. The concret form of step function is step(parameter,time1,position1,time2,position2),the parameter here is time.The component is in position1 at time1.The component is in position2 at time2.At the same time, the utilization of combined step functions ,which means multiply step functions are add to components , can realize various motions at different time.The step movement is achieved consequently

An Overview of Evolutionary Algorithms for Parameter Optimization

1993 ◽  
Vol 1 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Thomas Bäck ◽  
Hans-Paul Schwefel
Keyword(s):  
Evolutionary Algorithms ◽  
Step Function ◽  
Test Functions ◽  
Natural Evolution ◽  
Basic Algorithm ◽  
Research Questions ◽  
Selection Operator ◽  
Representation Scheme ◽  
High Level ◽  
Theoretical Results

Three main streams of evolutionary algorithms (EAs), probabilistic optimization algorithms based on the model of natural evolution, are compared in this article: evolution strategies (ESs), evolutionary programming (EP), and genetic algorithms (GAs). The comparison is performed with respect to certain characteristic components of EAs: the representation scheme of object variables, mutation, recombination, and the selection operator. Furthermore, each algorithm is formulated in a high-level notation as an instance of the general, unifying basic algorithm, and the fundamental theoretical results on the algorithms are presented. Finally, after presenting experimental results for three test functions representing a unimodal and a multimodal case as well as a step function with discontinuities, similarities and differences of the algorithms are elaborated, and some hints to open research questions are sketched.

Sign in / Sign up

Export Citation Format

Share Document