A FRAMEWORK FOR FORM-BASED CONCEPTUAL DESIGN IN STRUCTURAL ENGINEERING by Michael Gedig B.A.Sc., The University of British Columbia, 1992 M.A.Sc., The University of British Columbia, 1995 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Civil Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2010 © Michael Gedig, 2010 Abstract Conceptual structural design is a process through which structural forms are created. The forms are shaped by a set of design requirements representing the expected function, and by constraints that reflect physical laws and practical limitations. There is no direct mathematical transformation from requirements to a form; the conceptual design process is nonlinear and iterative. Like all creative processes, it is most effective when ideas can be rapidly synthesized, dissolved, combined and evolved. In structural design, these ideas need to be evaluated in the context of performance, functionality, and cost. Conceptual design, compared to later design stages, is characterized by a high degree of uncertainty and a general lack of knowledge. A key objective in conceptual structural design is therefore to rapidly create, modify and evaluate vague or abstract structural forms. This work describes a computational framework to support conceptual structural design, emphasizing the importance of form. Techniques from image processing, pattern recognition and linguistics are used to describe, classify, and reason with forms at high levels of abstraction. Most other computer applications in conceptual structural design describe design concepts in terms of words or through simplified spatial relationships. This work highlights the central role that visual information plays in formulating ideas in conceptual design. The major contributions of this work are an efficient method for synthesizing conceptual designs of discrete structures, and the application of pattern recognition and visual case- based reasoning techniques to conceptual structural design. The framework is directed towards large-scale discrete structures characterized by interconnected linear elements. During synthesis, forms are initially created using topology optimization methods; these forms are processed to extract high level information that supports further structural optimization, including the assessment of stability and relative cost. The high level information is used to describe, classify and store conceptual forms for case-based reasoning. A novel feature of the work is that arbitrary images of shapes may be interpreted as structures by using visual similarity to infer potential boundary conditions, functionality, and behaviour for those shapes. ii Abstract This dissertation gives a complete description of the framework, along with sample applications. A proof-of-concept computer application is also described. iii Table of Contents Abstract............................................................................................................................... ii Table of Contents...............................................................................................................iv List of Tables .................................................................................................................... vii List of Figures..................................................................................................................viii Acknowledgements............................................................................................................ xi 1. Introduction.................................................................................................................1 2. Background................................................................................................................. 6 2.1. Conceptual Design.............................................................................................. 6 2.1.1. Expert Systems............................................................................................ 7 2.1.2. Qualitative Reasoning................................................................................. 8 2.1.3. Design Prototypes....................................................................................... 8 2.1.4. Case-based Reasoning.............................................................................. 10 2.1.5. Building Design........................................................................................ 14 2.1.6. Commercial Software............................................................................... 15 2.1.7. Visual Case-Based Reasoning .................................................................. 16 2.1.8. User Interfaces.......................................................................................... 19 2.1.9. Mechanical Design....................................................................................20 2.1.10. Conceptual Analysis Methods.................................................................. 20 2.2. Optimization ..................................................................................................... 21 2.2.1. General Optimization................................................................................ 21 2.2.2. Multiobjective Optimization..................................................................... 23 2.2.3. Structural Optimization............................................................................. 24 2.2.4. Postprocessing........................................................................................... 33 2.3. Image Processing.............................................................................................. 34 2.3.1. General...................................................................................................... 34 2.3.2. Morphology............................................................................................... 35 2.3.3. Thinning.................................................................................................... 37 2.3.4. Distance Map............................................................................................ 37 2.3.5. Hit-or-Miss Operators............................................................................... 38 2.3.6. Projection .................................................................................................. 38 iv Table of Contents 2.3.7. Hough Transform...................................................................................... 39 2.3.8. Fourier Transform..................................................................................... 41 2.4. Pattern Recognition........................................................................................... 41 2.4.1. Overview................................................................................................... 41 2.4.2. Regions ..................................................................................................... 42 2.4.3. Boundaries and Curves............................................................................. 43 2.4.4. Structural Descriptions.............................................................................. 43 2.4.5. Relational Graphs...................................................................................... 45 2.4.6. Output ....................................................................................................... 46 2.4.7. Graph Matching........................................................................................ 47 2.5. Structural Stability ............................................................................................ 49 2.5.1. Maxwell’s Rule......................................................................................... 50 2.5.2. Gruebler’s Equation.................................................................................. 50 2.5.3. Static and Kinematic Indeterminacy......................................................... 51 2.5.4. Linear Structural Analysis ........................................................................ 51 2.5.5. Equilibrium matrix analysis...................................................................... 53 2.5.6. Mechanisms .............................................................................................. 54 2.6. Summary........................................................................................................... 55 3. Framework ................................................................................................................ 58 3.1. Overview........................................................................................................... 58 3.2. Synthesis Phase................................................................................................. 61 3.2.1. Design Formulation.................................................................................. 62 3.2.2. Representation Model............................................................................... 63 3.2.3. Topology Optimization............................................................................. 65 3.2.4. Image Processing...................................................................................... 69 3.2.5. Relational Graph ....................................................................................... 74 3.2.6. Discussion................................................................................................