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E-raamat: Discrete Optimization in Architecture: Extremely Modular Systems

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This book is comprised of two parts, both of which explore modular systems: Pipe-Z (PZ) and Truss-Z (TZ), respectively. It presents several methods of creating PZ and TZ structures subjected to discrete optimization. The algorithms presented employ graph-theoretic and heuristic methods. The underlying idea of both systems is to create free-form structures using the minimal number of types of modular elements. PZ is more conceptual, as it forms single-branch mathematical knots with a single type of module. Conversely, TZ is a skeletal system for creating free-form pedestrian ramps and ramp networks among any number of terminals in space. In physical space, TZ uses two types of modules that are mirror reflections of each other. The optimization criteria discussed include: the minimal number of units, maximal adherence to the given guide paths, etc.
Part I Pipe-Z
1 Introduction
3(8)
1.1 Introduction
3(3)
1.1.1 The Pipe-Z Module
5(1)
1.2 Alignment of Modules Along a Guide Path
6(5)
1.2.1 Self-intersections
8(1)
1.2.2 Reduction of the Number of Twist Angles k
8(1)
References
9(2)
2 Pipe-Z Optimization
11(8)
2.1 Introduction
11(1)
2.2 Trapezoid-Tiling of a Planar Unknot
12(2)
2.2.1 Alignment of Trapezoidal Units to the Guide Path
13(1)
2.3 Random Search
14(1)
2.3.1 Domain Visualization
14(1)
2.4 Optimization of a PZ Knot 63
15(4)
References
17(2)
3 Pipe-Z Manipulatives
19(12)
3.1 Introduction
19(1)
3.2 Virtual Pipe-Z Manipulatives
20(3)
3.2.1 Virtual PZ Knotting
21(2)
3.3 Physical Pipe-Z Manipulatives
23(8)
3.3.1 Fabrication of the Physical Model of Pipe-Z Module
25(4)
References
29(2)
4 Arm-Z
31(6)
4.1 Introduction
31(1)
4.2 Extension
32(1)
4.3 Translation
32(1)
4.4 Flexure
33(4)
References
35(2)
5 Deployable Pipe-Z
37(10)
5.1 Introduction
37(1)
5.2 Foldable Pipe-Z Module (fPZM)
38(6)
5.2.1 Folding Analysis of fPZM
38(2)
5.2.2 Folding of a Multi-module Deployable Pipe-Z (dPZ)
40(1)
5.2.3 "Outside-In"
41(1)
5.2.4 "Inside-Out"
42(1)
5.2.5 Collapsible Concentric Toric Rings
43(1)
5.3 Low-Fidelity Prototype of Deployable Pipe-Z
44(3)
References
44(3)
Part II Truss-Z
6 Introduction
47(22)
6.1 Modularity Versus Free-Form
47(3)
6.2 Truss-Z as a Ramp
50(2)
6.3 Truss-Z Module (TZM)
52(1)
6.4 Preliminary Static Analysis of TZM
53(5)
6.4.1 Topological Properties of TZM
54(2)
6.4.2 Rigidity of TZM
56(1)
6.4.3 Truss-Z as an Earthquake-Resistant Structure
57(1)
6.5 Deployable Truss-Z
58(1)
6.5.1 Foldable TZM (fTZM)
58(1)
6.6 Fabrication of TZM
58(11)
6.6.1 Template System
61(3)
6.6.2 The Resin Casting
64(3)
References
67(2)
7 Single-Branch Truss-Z (STZ)
69(36)
7.1 Alignment of STZ to the Given Path
69(2)
7.2 Backtracking
71(6)
7.2.1 Case Study I
73(4)
7.3 Optimization of STZ
77(6)
7.3.1 Encoding of STZ Planar Layout
78(1)
7.3.2 Objective (cost) Function
78(2)
7.3.3 Calibration of Weights for the Cost Function
80(1)
7.3.4 Tournament Selection
81(1)
7.3.5 Mutation
82(1)
7.3.6 Stop Criterion
83(1)
7.4 Evolution Strategy
83(3)
7.5 Genetic Algorithm (GA)
86(4)
7.5.1 Recombination
86(1)
7.5.2 GA with Uniform Crossover (GAUX)
86(1)
7.5.3 GA with One-Point Crossover (GAOPX)
87(1)
7.5.4 Interpretation of the Results
88(2)
7.6 Graph-Theoretical Method
90(11)
7.6.1 The GT Experiment
95(1)
7.6.2 Can a TZ Path Be Even Shorter?
96(2)
7.6.3 Case Study II
98(3)
7.7 The Supporting Structure
101(4)
References
103(2)
8 Multi-branch Truss-Z (MTZ)
105(16)
8.1 Creation of a MTZ Network
105(1)
8.2 Alignment of MTZ to Given Paths
106(2)
8.3 Backtracking for MTZ
108(1)
8.4 Optimization of MTZ with Evolution Strategy
109(1)
8.5 Transformation Operators
110(3)
8.5.1 Transformation of MTZC to M7Z6
113(1)
8.6 A Quasi-Optimization
113(4)
8.6.1 Evolution Strategy-Based Experiment (ES)
114(3)
8.7 Case Study III
117(4)
8.7.1 The Results
118(2)
Reference
120(1)
Glossary 121
Dr. Machi Zawidzkis doctoral research focused on various optimization methods based on CI for the fundamental problems of the architectural design: Functionality, Structure and Aesthetics. His research interests are in designing built environment, especially in ergonomics and architectural design.
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