Preface |
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xi | |
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1.1 Structural Optimization (SO) |
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1 | (1) |
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1.2 Topology Optimization |
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2 | (8) |
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1.2.1 Homogenization Method for Topology Optimization |
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4 | (1) |
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1.2.2 Solid Isotropic Material with Penalization (SIMP) |
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5 | (1) |
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1.2.3 Fully Stressed Design (FSD) |
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6 | (1) |
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1.2.4 Computer-Aided Shape Optimization (CAO) |
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7 | (1) |
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1.2.5 Soft Kill Option (SKO) |
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8 | (1) |
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1.2.6 Evolutionary Structural Optimization (ESO) |
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9 | (1) |
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1.2.7 Bidirectional ESO (BESO) |
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9 | (1) |
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10 | (5) |
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12 | (3) |
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2 Growth Method for the Size, Topology, and Geometry Optimization of Truss Structures |
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15 | (1) |
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16 | (2) |
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18 | (1) |
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2.4 Topology and Size Optimization |
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18 | (1) |
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2.5 Geometry Optimization |
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19 | (2) |
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2.6 Optimality Verification |
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21 | (1) |
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22 | (1) |
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2.8 Practical Criteria to Limit the Number of Added Bars to New Joints |
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23 | (4) |
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2.8.1 Limiting the Number of Crossed Bars |
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23 | (1) |
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2.8.2 Using Orthogonality and Maximum Degree of Indeterminacy |
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24 | (1) |
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25 | (2) |
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3 Discrete Method of Structural Optimization |
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27 | (1) |
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3.2 The Sequential Element Rejection and Admission (SERA) Algorithm |
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28 | (3) |
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3.3 Definition of the Objective Function |
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31 | (3) |
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3.3.1 Stress-Based Objective Function |
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31 | (1) |
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3.3.2 Compliant-Based Objective Function |
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32 | (1) |
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3.3.3 Multiple-Criteria Objective Function |
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32 | (1) |
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3.3.4 Mutual Potential Energy Objective Function |
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33 | (1) |
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34 | (2) |
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3.4.1 The Limit Volume Fraction |
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34 | (1) |
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3.4.2 Controlling the Rate of Material Admission and Removal |
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34 | (1) |
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3.4.3 The Smoothing Ratio |
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35 | (1) |
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3.4.4 The Material Redistribution Fraction |
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35 | (1) |
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35 | (1) |
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36 | (1) |
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3.5 The Initial Design Domain |
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36 | (1) |
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3.6 The Volume Fraction to be Redistributed |
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36 | (2) |
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3.6.1 Determine the Volume Fraction to be Rearranged |
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37 | (1) |
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3.6.2 Material Redistribution |
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38 | (1) |
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3.7 The Finite Element Analysis |
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38 | (1) |
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3.8 The Elemental Criterion Value |
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39 | (4) |
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3.8.1 Elemental Criterion for a Fully Stressed Design |
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39 | (1) |
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3.8.2 Elemental Criterion for Minimum Compliance |
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40 | (1) |
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3.8.3 Elemental Criterion for Multiple Criteria |
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41 | (1) |
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3.8.4 Elemental Criterion for Compliant Mechanisms |
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42 | (1) |
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3.9 Mesh Independent Filtering |
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43 | (1) |
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3.10 Convergence Criterion |
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44 | (3) |
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44 | (2) |
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46 | (1) |
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4 Continuous Method of Structural Optimization |
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47 | (1) |
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4.2 The Isolines Topology Design Algorithm |
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48 | (1) |
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4.3 The Optimization Problem |
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49 | (3) |
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4.3.1 Criterion Selection |
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50 | (1) |
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4.3.2 Criterion for Problems with Different Tensile and Compressive Structural Behaviour |
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50 | (1) |
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4.3.3 Nondesign Domain Region |
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51 | (1) |
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52 | (1) |
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4.4.1 Target Final Design Volume |
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52 | (1) |
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4.4.2 Total Number of Iterations |
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52 | (1) |
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4.4.3 Total Number of Load Cases |
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52 | (1) |
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4.4.4 Total Number of Material Phases |
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52 | (1) |
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4.4.5 The Weighting Factor for the Different Material Phases |
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53 | (1) |
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4.4.6 The Minimum Volume Change Limit |
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53 | (1) |
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4.5 Analysis of the Design Domain |
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53 | (7) |
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4.5.1 Fixed Grid Finite Element Method |
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54 | (1) |
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4.5.2 Calculating the Elemental Criterion Value |
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55 | (1) |
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4.5.3 Calculating the Nodal Criterion Value |
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56 | (1) |
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4.5.4 Initial Design Domain Analysis |
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56 | (3) |
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4.5.5 Reanalysis of the Design Domain Analysis |
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59 | (1) |
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4.6 Determining the Target Volume |
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60 | (1) |
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4.7 Determining the Minimum Criterion Level (MCL) |
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61 | (4) |
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4.7.1 MCL for Single Load Case Problems |
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61 | (1) |
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4.7.2 MCL for Multiple Load Case Problems |
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61 | (2) |
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4.7.3 MCL for Multiple Material Phases Problems |
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63 | (2) |
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4.8 Determination of the Structural Shape or Surface |
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65 | (3) |
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4.8.1 Determination of the Isolines for 2D Problems |
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66 | (1) |
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4.8.2 Determination of the Isosurfaces for 3D Problems |
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67 | (1) |
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4.9 Structural Boundary Stabilization |
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68 | (3) |
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68 | (3) |
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5 Hands-On Applications of Structural Optimization |
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71 | (1) |
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72 | (1) |
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5.3 Messerschmidt-Bolkow-Blohm Beam |
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73 | (3) |
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5.4 Michell Cantilever with Fixed Circular Boundary |
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76 | (2) |
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5.5 Michell Beam with Fixed Supports |
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78 | (2) |
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5.6 Michell Beam with Roller Support |
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80 | (3) |
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83 | (1) |
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5.8 Michell Beam with Roller Support and Multiple Load Cases |
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84 | (1) |
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85 | (2) |
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87 | (1) |
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88 | (1) |
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89 | (4) |
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91 | (2) |
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6 Topology Optimization as a Digital Design Tool |
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93 | (2) |
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6.2 Effect of Different Load Angle on a Michell Cantilever |
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95 | (2) |
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97 | (1) |
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6.4 Exercise Bar Support Arm |
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98 | (3) |
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6.5 Hemispherical Dome Structure |
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101 | (1) |
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6.6 Bridge Structure with Nondesign Domain |
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102 | (2) |
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104 | (2) |
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6.8 Double-Sided Beam-to-Column Joint |
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106 | (1) |
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107 | (2) |
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109 | (4) |
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110 | (3) |
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7 User Guides for Enclosed Software |
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113 | (1) |
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7.2 Truss Topology Optimization (TTO) Program |
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113 | (11) |
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7.2.1 System Requirements and Installation of TTO |
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113 | (2) |
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7.2.2 Overview of the TTO Graphical User Interface |
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115 | (9) |
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7.3 Step-by-Step Guide to Use TTO |
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124 | (5) |
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124 | (2) |
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7.3.2 TTO Models in the Included Files |
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126 | (3) |
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7.4 SERA Topology Optimization Program |
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129 | (8) |
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130 | (7) |
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7.5 Modifying the SERA Code to Solve Different Examples |
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137 | (10) |
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7.5.1 The Messerschmidt-Bolkow-Blohm Beam (MBB) |
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137 | (1) |
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7.5.2 The Michell Cantilever |
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137 | (1) |
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7.5.3 Multiple Load Case Problem |
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138 | (3) |
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7.5.4 Structures with Passive Elements |
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141 | (3) |
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7.5.5 Compliant Mechanism Problems |
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144 | (3) |
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7.6 Isolines Topology Design Program (liteITD) |
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147 | (23) |
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7.6.1 System Requirements and Installation of liteITD Software |
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148 | (1) |
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7.6.2 Overview of the liteITD Interface |
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149 | (21) |
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7.7 Step-by-Step Guide to Use liteITD |
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170 | (9) |
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7.7.1 Define the Design Workbench Dimensions |
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172 | (1) |
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7.7.2 Draw the Geometric Model |
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172 | (2) |
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7.7.3 Specify the Material Properties |
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174 | (1) |
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7.7.4 Generate the Finite Element Mesh |
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175 | (1) |
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7.7.5 Apply the DOF Constraints |
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175 | (2) |
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7.7.6 Apply the Loading Conditions |
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177 | (1) |
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7.7.7 Specify the liteITD Parameters and Run Optimization |
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178 | (1) |
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7.7.8 View the Resulting Optimal Design |
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179 | (1) |
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7.8 Additional liteITD Examples |
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179 | (4) |
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7.8.1 Michell Cantilever under Multiple Loading Conditions |
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179 | (1) |
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7.8.2 Michell Cantilever with Different Properties in Tension and Compression |
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180 | (2) |
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7.8.3 Michell Cantilever Using Multimaterials |
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182 | (1) |
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7.9 Appropriate Equivalent Units |
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183 | (2) |
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184 | (1) |
Index |
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185 | |