Preface |
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xi | |
Authors |
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xiii | |
1 Introduction |
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1 | (20) |
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1 | (3) |
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1 | (1) |
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1.1.2 Finite Element Applications in Engineering |
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1 | (2) |
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1.1.3 FEA with ANSYS Workbench |
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3 | (1) |
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1.1.4 A Brief History of FEA |
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3 | (1) |
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1.1.5 A General Procedure for FEA |
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4 | (1) |
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1.2 An Example in FEA: Spring System |
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4 | (9) |
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5 | (1) |
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6 | (3) |
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1.2.2.1 Assembly of Element Equations: Direct Approach |
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6 | (2) |
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1.2.2.2 Assembly of Element Equations: Energy Approach |
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8 | (1) |
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1.2.3 Boundary and Load Conditions |
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9 | (1) |
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1.2.4 Solution Verification |
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10 | (1) |
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10 | (3) |
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1.3 Overview of ANSYS Workbench |
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13 | (4) |
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13 | (1) |
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14 | (1) |
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1.3.3 The Project Schematic |
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14 | (2) |
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16 | (1) |
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16 | (1) |
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17 | (1) |
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18 | (3) |
2 Bars and Trusses |
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21 | (44) |
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21 | (1) |
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2.2 Review of the 1-D Elasticity Theory |
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21 | (1) |
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22 | (1) |
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2.4 Formulation of the Bar Element |
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23 | (9) |
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2.4.1 Stiffness Matrix: Direct Method |
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23 | (2) |
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2.4.2 Stiffness Matrix: Energy Approach |
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25 | (2) |
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2.4.3 Treatment of Distributed Load |
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27 | (1) |
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2.4.4 Bar Element in 2-D and 3-D |
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28 | (3) |
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28 | (3) |
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31 | (1) |
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31 | (1) |
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2.5 Examples with Bar Elements |
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32 | (8) |
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2.6 Case Study with ANSYS Workbench |
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40 | (19) |
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59 | (1) |
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2.8 Review of Learning Objectives |
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59 | (1) |
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59 | (6) |
3 Beams and Frames |
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65 | (52) |
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65 | (1) |
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3.2 Review of the Beam Theory |
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65 | (3) |
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3.2.1 Euler-Bernoulli Beam and Timoshenko Beam |
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65 | (2) |
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3.2.2 Stress, Strain, Deflection, and Their Relations |
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67 | (1) |
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3.3 Modeling of Beams and Frames |
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68 | (2) |
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3.3.1 Cross Sections and Strong/Weak Axis |
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68 | (1) |
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69 | (1) |
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3.3.3 Conversion of a Physical Model into a Line Model |
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70 | (1) |
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3.4 Formulation of the Beam Element |
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70 | (6) |
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3.4.1 Element Stiffness Equation: The Direct Approach |
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71 | (1) |
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3.4.2 Element Stiffness Equation: The Energy Approach |
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72 | (2) |
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3.4.3 Treatment of Distributed Loads |
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74 | (1) |
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3.4.4 Stiffness Matrix for a General Beam Element |
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75 | (1) |
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3.5 Examples with Beam Elements |
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76 | (9) |
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3.6 Case Study with ANSYS Workbench |
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85 | (27) |
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112 | (1) |
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3.8 Review of Learning Objectives |
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112 | (1) |
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112 | (5) |
4 Two-Dimensional Elasticity |
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117 | (44) |
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117 | (1) |
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4.2 Review of 2-D Elasticity Theory |
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117 | (5) |
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117 | (1) |
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118 | (1) |
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4.2.3 Stress-Strain (Constitutive) Equations |
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119 | (1) |
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4.2.4 Strain and Displacement Relations |
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120 | (1) |
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4.2.5 Equilibrium Equations |
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121 | (1) |
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4.2.6 Boundary Conditions |
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121 | (1) |
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4.2.7 Exact Elasticity Solution |
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121 | (1) |
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4.3 Modeling of 2-D Elasticity Problems |
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122 | (1) |
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4.4 Formulation of the Plane Stress/Strain Element |
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123 | (14) |
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4.4.1 A General Formula for the Stiffness Matrix |
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124 | (1) |
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4.4.2 Constant Strain Triangle (CST or T3) |
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124 | (5) |
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4.4.3 Quadratic Triangular Element (LST or T6) |
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129 | (1) |
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4.4.4 Linear Quadrilateral Element (Q4) |
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130 | (1) |
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4.4.5 Quadratic Quadrilateral Element (Q8) |
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131 | (1) |
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4.4.6 Transformation of Loads |
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132 | (2) |
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134 | (2) |
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4.4.7.1 The von Mises Stress |
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134 | (1) |
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4.4.7.2 Averaged Stresses |
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135 | (1) |
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4.4.8 General Comments on the 2-D Elements |
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136 | (1) |
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4.5 Case Study with ANSYS Workbench |
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137 | (18) |
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155 | (1) |
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4.7 Review of Learning Objectives |
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155 | (1) |
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156 | (5) |
5 Modeling and Solution Techniques |
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161 | (26) |
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161 | (1) |
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161 | (2) |
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162 | (1) |
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5.3 Substructures (Superelements) |
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163 | (1) |
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164 | (2) |
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5.4.1 Direct Methods (Gauss Elimination) |
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164 | (1) |
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164 | (1) |
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5.4.3 An Example: Gauss Elimination |
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164 | (1) |
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5.4.4 An Example: Iterative Method |
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165 | (1) |
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5.5 Nature of Finite Element Solutions |
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166 | (1) |
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5.6 Convergence of FEA Solutions |
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167 | (1) |
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5.7 Adaptivity (h-, p-, and hp-Methods) |
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167 | (1) |
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5.8 Case Study with ANSYS Workbench |
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168 | (14) |
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182 | (1) |
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5.10 Review of Learning Objectives |
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183 | (1) |
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183 | (4) |
6 Plate and Shell Analyses |
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187 | (32) |
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187 | (1) |
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6.2 Review of Plate Theory |
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187 | (7) |
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6.2.1 Force and Stress Relations in Plates |
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187 | (2) |
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6.2.2 Thin Plate Theory (Kirchhoff Plate Theory) |
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189 | (3) |
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6.2.2.1 Example: A Thin Plate |
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191 | (1) |
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6.2.3 Thick Plate Theory (Mindlin Plate Theory) |
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192 | (1) |
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193 | (2) |
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6.2.4.1 Shell Example: A Cylindrical Container |
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193 | (1) |
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6.3 Modeling of Plates and Shells |
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194 | (1) |
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6.4 Formulation of the Plate and Shell Elements |
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195 | (4) |
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6.4.1 Kirchhoff Plate Elements |
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195 | (1) |
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6.4.2 Mindlin Plate Elements |
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196 | (1) |
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6.4.3 Discrete Kirchhoff Elements |
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197 | (1) |
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6.4.4 Flat Shell Elements |
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197 | (1) |
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6.4.5 Curved Shell Elements |
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198 | (1) |
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6.5 Case Studies with ANSYS Workbench |
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199 | (15) |
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214 | (1) |
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6.7 Review of Learning Objectives |
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214 | (1) |
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214 | (5) |
7 Three-Dimensional Elasticity |
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219 | (42) |
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219 | (1) |
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7.2 Review of Theory of Elasticity |
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219 | (3) |
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7.2.1 Stress-Strain Relation |
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220 | (1) |
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221 | (1) |
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7.2.3 Strain-Displacement Relation |
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221 | (1) |
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7.2.4 Equilibrium Equations |
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221 | (1) |
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7.2.5 Boundary Conditions |
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222 | (1) |
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222 | (1) |
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7.3 Modeling of 3-D Elastic Structures |
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222 | (3) |
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7.3.1 Mesh Discretization |
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223 | (1) |
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7.3.2 Boundary Conditions: Supports |
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223 | (1) |
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7.3.3 Boundary Conditions: Loads |
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224 | (1) |
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7.3.4 Assembly Analysis: Contacts |
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224 | (1) |
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7.4 Formulation of Solid Elements |
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225 | (5) |
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7.4.1 General Formulation |
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225 | (1) |
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7.4.2 Typical Solid Element Types |
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226 | (1) |
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7.4.3 Formulation of a Linear Hexahedral Element Type |
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227 | (3) |
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7.4.4 Treatment of Distributed Loads |
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230 | (1) |
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7.5 Case Studies with ANSYS Workbench |
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230 | (25) |
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255 | (1) |
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7.7 Review of Learning Objectives |
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255 | (1) |
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255 | (6) |
8 Structural Vibration and Dynamics |
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261 | (40) |
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261 | (1) |
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8.2 Review of Basic Equations |
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261 | (6) |
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8.2.1 A Single DOF System |
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262 | (2) |
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264 | (3) |
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264 | (2) |
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266 | (1) |
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8.3 Formulation for Modal Analysis |
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267 | (4) |
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269 | (2) |
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8.4 Formulation for Frequency Response Analysis |
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271 | (1) |
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271 | (1) |
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272 | (1) |
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8.5 Formulation for Transient Response Analysis |
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272 | (3) |
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8.5.1 Direct Methods (Direct Integration Methods) |
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273 | (1) |
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274 | (1) |
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275 | (2) |
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275 | (1) |
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8.6.2 Frequency Response Analysis |
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276 | (1) |
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8.6.3 Transient Response Analysis |
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276 | (1) |
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8.6.4 Cautions in Dynamic Analysis |
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276 | (1) |
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8.7 Case Studies with ANSYS Workbench |
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277 | (16) |
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293 | (1) |
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8.9 Review of Learning Objectives |
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294 | (1) |
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294 | (7) |
9 Thermal Analysis |
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301 | (36) |
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301 | (1) |
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9.2 Review of Basic Equations |
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301 | (5) |
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301 | (2) |
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9.2.1.1 Finite Element Formulation for Heat Conduction |
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303 | (1) |
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9.2.2 Thermal Stress Analysis |
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303 | (3) |
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304 | (1) |
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305 | (1) |
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305 | (1) |
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9.2.2.4 Notes on FEA for Thermal Stress Analysis |
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305 | (1) |
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9.3 Modeling of Thermal Problems |
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306 | (2) |
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306 | (1) |
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9.3.2 Thermal Stress Analysis |
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306 | (2) |
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9.4 Case Studies with ANSYS Workbench |
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308 | (22) |
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330 | (1) |
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9.6 Review of Learning Objectives |
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330 | (1) |
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330 | (7) |
10 Introduction to Fluid Analysis |
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337 | (36) |
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337 | (1) |
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10.2 Review of Basic Equations |
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337 | (2) |
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10.2.1 Describing Fluid Motion |
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337 | (1) |
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10.2.2 Types of Fluid Flow |
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337 | (1) |
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10.2.3 Navier-Stokes Equations |
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338 | (1) |
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10.3 Modeling of Fluid Flow |
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339 | (2) |
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339 | (1) |
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339 | (1) |
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10.3.3 Boundary Conditions |
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339 | (1) |
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10.3.4 Solution Visualization |
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340 | (1) |
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10.4 Case Studies with ANSYS Workbench |
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341 | (27) |
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368 | (1) |
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10.6 Review of Learning Objectives |
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368 | (1) |
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368 | (5) |
11 Design Optimization |
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373 | (46) |
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373 | (1) |
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11.2 Topology Optimization |
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373 | (1) |
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11.3 Parametric Optimization |
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374 | (1) |
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11.4 Design Space Exploration for Parametric Optimization |
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374 | (3) |
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11.4.1 Design of Experiments |
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375 | (2) |
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11.4.2 Response Surface Optimization |
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377 | (1) |
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11.5 Case Studies with ANSYS Workbench |
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377 | (38) |
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415 | (1) |
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11.7 Review of Learning Objectives |
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415 | (1) |
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415 | (4) |
12 Failure Analysis |
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419 | (22) |
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419 | (1) |
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419 | (2) |
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419 | (1) |
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12.2.1.1 Maximum Shear Stress Theory (Tresca Criterion) |
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419 | (1) |
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12.2.1.2 Distortion Energy Theory (von Mises Criterion) |
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420 | (1) |
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420 | (1) |
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12.2.2.1 Maximum Normal Stress Theory |
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420 | (1) |
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12.2.2.2 Mohr-Coulomb Theory |
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420 | (1) |
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421 | (3) |
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12.3.1 Soderberg Failure Criterion |
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422 | (1) |
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12.3.2 Goodman Failure Criterion |
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422 | (1) |
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12.3.3 Gerber Failure Criterion |
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423 | (1) |
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424 | (1) |
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12.5 Case Studies with ANSYS Workbench |
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425 | (11) |
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436 | (1) |
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12.7 Review of Learning Objectives |
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436 | (1) |
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437 | (4) |
Appendix 1: Review of Matrix Algebra |
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441 | (6) |
Appendix 2: Photo Credits |
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447 | (2) |
References |
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449 | (2) |
Index |
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