Aircraft Concepts Modeling with Subdivision Surfaces

Pametrically Controlled Subdivision Surfaces for Conceptual Design

Engineering design: A systematic approach

This paper describes a method for recursively generating surfaces that approximate points lying-on a mesh of arbitrary topology. The method is presented as a generalization of a recursive bicubic B-spline patch subdivision algorithm. For rectangular control-point meshes, the method generates a standard B-spline surface. For non-rectangular meshes, it generates surfaces that are shown to reduce to a standard B-spline surface except at a small number of points, called extraordinary points. Therefore, everywhere except at these points the surface is continuous in tangent and curvature. At the extraordinary points, the pictures of the surface indicate that the surface is at least continuous in tangent, but no proof of continuity is given. A similar algorithm for biquadratic B-splines is also presented.

Recursively generated B-spline surfaces on arbitrary topological meshes

Preface Acknowledgement On the MIT-Pappalardo Series of Mechanical Engineering Books On CIRP Design Book Series 1. Introduction to Axiomatic Design 1.1 Introduction 1.2 Current State of Design Practice 1.3 Who Are the Designers? How Do We Design? What Is Design? 1.4 What Is the Ultimate Goal of Axiomatic Design? 1.5 Role of Axioms in Development of Science and Technology - A Technological Perspective 1.6 Axiomatic Approach vs. Algorithmic Approach 1.7 Axiomatic Design Framework 1.8 Common Mistakes Made by Designers 1.9 Comparison of Axiomatic Design with Other Methodologies 1.10 Summary References Appendix 1-A Corollaries and Theorems Homework 2. One-FR Design, the Information Axiom, and Robust Design 2.1 Introduction 2.2 Introduction to One-FR Design 2.3 Design Issues for the One-FR Design 2.4 One-FR Design and Information Content 2.5 Elimination of Bias and Reduction of Variance 2.6 Robust Design 2.7 Design Process 2.8 Summary References Appendices 2-A Pressure in Thick Wall Tube 2-B Discrete Random Variables: Expected Value, Variance, and Standard Deviation 2-C Continuous Random Variables: Expected Value, Variance, Standard Deviation, and Multivariate Random Variables Homework 3. Multi-FR Design 3.1 Introduction 3.2 Brief Review of Axiomatic Theory for Multi-FR Design 3.3 The Independence Axiom and the Information Axiom - Their Implications for a Multi-FR Design Task 3.4 On Ideal Multi-FR Design 3.5 Uncoupled and Decoupled Multi-FR Designs 3.6 Information Content and Complexity of Multi-FR Design 3.7 Integration of DPs to Minimize the Information Content 3.8 Nonlinear Multi-FR Design 3.9 Design of Dispatching and Schedules: Avoiding Traffic Congestion 3.10 Conclusions References Appendix 3-A Independence of the Two Design Axioms Appendix 3-B Corollaries and Theorems Related to Information and Complexity Homework 4. Design of Systems 4.1 Introduction 4.2 Issues Related to System Design 4.3 Classification of Systems 4.4 Axiomatic Design Thoery for Fixed Systems 4.5 Design and Operation of Large Systems 4.6 Representation of the System Architecture of Fixed Systems 4.7 Mathematical Modeling, Simulation, and Optimization of Systems 4.8 Application of the System Architecture 4.9 On human-machine Interface 4.10 Generation of System Architecture using Computer Science 4.11 Conclusions References Homework 5. Axiomatic Design of Software 5.1 Introduction 5.2 Axiomatic Design 5.3 Design of a Software System for a Library: An Example 5.4 Software for Design of a Rib in Injection Molding of Plastic Parts: an Example (Adapted from Kim, et al., 1991) 5.5 Axiomatic Design of Object-Oriented Software System 5.6 Case Study: Acclaro Software - Axiomatic Design of Object-Oriented Software System (ADo-oSS) for Designers 5.7 Case Study: Software Design for Real Time Control of Hardware/Software System 5.8 Software Development for Design Automation for Glass-Bulb Design 5.9 An Ideal Software System 5.10 Other Issues Related to Software Design 5.11 Conclusions References Homework 6. Axiomatic Design of Manufacturing Systems 6.1 Introduction 6.2 Basic Requirements of a Manufacturing System 6.3 Elements of Manufacturing Systems 6.4 Axiomatic Design of Fixed Manufacturing Systems for Identical Parts 6.5 Axiomatic Design of a Flexible Manufacturing System for Different Part 6.6 Mathematical Modeling and Optimization of Design 6.7 Representation of Manufacturing System Architecture 6.8 Conculsions References Homework 7. Axiomatic Design of Materals and Materials Processing Techniques Summary of Chapter 7 7.1 Introduction 7.2 Mixalloys 7.3 Microcellular Plastics 7.4 Layered Manufacturing Process 7.5 Conclusions References Homework 8. Product Development Summary of Chapter 8 8.1 Introduction 8.2 Mapping from the Customer Domain to the Functional Domain 8.3 Mapping from FRs to DPs 8.4 Application of the Information Axiom 8.5 Case Study - Depth Charge 8.6 Concurrent Engineering - Mapping from FR to DP to PV 8.7 Product Service 8.8 System Architecture 8.9 Conclusions References Homework 9. A Theory of Complexity - The Design Axioms, Information, Complexity, and Periodicity Summary of Chapter 9 9.1 Introduction 9.2 Complexity, Uncertainty, Information, and Periodicity 9.3 Reduction of Uncertainity - Conversion of a Design with Time-Dependent Combinatorial Complexity to a Design with Time-Dependent Periodic Complexity 9.4 Distinction between Time-Independent and Time-Dependent Complexity 9.5 Other Implications of Periodic Complexity - A Speculation 9.6 Conclusion Remarks References Homework INDEX

Axiomatic Design: Advances And Applications

The behaviour of the limits surface defined by a recursive division construction can be analysed in terms of the eigenvalues of a set of matrices. This analysis predicts effects actually observed, and leads to suggestions for the further improvement of the method.

Behaviour of recursive division surfaces near extraordinary points

The conceptual aircraft designer is faced with a dilemma, how to strike the best balance between productivity and fidelity? Historically, handbook methods have required only the coarsest of geometric parameterizations in order to perform analysis. Increasingly, there has been a drive to upgrade analysis methods, but these require considerably more precise and detailed geometry. Attempts have been made to use computer-aided design packages to fill this void, but their cost and steep learning curve have made them unwieldy at best. Vehicle Sketch Pad (VSP) has been developed over several years to better fill this void. While no substitute for the full feature set of computer-aided design packages, VSP allows even novices to quickly become proficient in defining three-dimensional, watertight aircraft geometries that are adequate for producing multi-disciplinary meta-models for higher order analysis methods, wind tunnel and display models, as well as a starting point for animation models. This paper will give an overview of the development and future course of VSP.

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Aircraft Concepts Modeling with Subdivision Surfaces

Citations

Pametrically Controlled Subdivision Surfaces for Conceptual Design

References

Engineering design: A systematic approach

Recursively generated B-spline surfaces on arbitrary topological meshes

Axiomatic Design: Advances And Applications

Behaviour of recursive division surfaces near extraordinary points

Vehicle Sketch Pad: a Parametric Geometry Modeler for Conceptual Aircraft Design

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