| Description |
1 online resource (172 pages) : Illustrations (some colored) |
|
text txt rdacontent |
|
computer c rdamedia |
|
online resource cr rdacarrier |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
Introduction ixPart 1. Multiscale Topology Optimization in the Context of Non-separated Scales 1Chapter 1. Size Effect Analysis in Topology Optimization for Periodic Structures Using the Classical Homogenization 31.1. The classical homogenization method 41.1.1. Localization problem 41.1.2. Definition and computation of the effective material properties 71.1.3. Numerical implementation for the local problem with PER 91.2. Topology optimization model and procedure 101.2.1. Optimization model and sensitivity number 101.2.2. Finite element meshes and relocalization scheme 121.2.3. Optimization procedure 141.3. Numerical examples 161.3.1. Doubly clamped elastic domain 171.3.2. L-shaped structure 191.3.3. MBB beam 241.4. Concluding remarks 25Chapter 2. Multiscale Topology Optimization of Periodic Structures Taking into Account Strain Gradient 292.1. Non-local filter-based homogenization for non-separated scales 302.1.1. Definition of local and mesoscopic fields through the filter 302.1.2. Microscopic unit cell calculations 332.1.3. Mesoscopic structure calculations 392.2. Topology optimization procedure 412.2.1. Model definition and sensitivity numbers 412.2.2. Overall optimization procedure 422.3. Validation of the non-local homogenization approach 432.4. Numerical examples 452.4.1. Cantilever beam with a concentrated load 462.4.2. Four-point bending lattice structure 522.5. Concluding remarks 55Chapter 3. Topology Optimization of Meso-structures with Fixed Periodic Microstructures 573.1. Optimization model and procedure 583.2. Numerical examples 613.2.1. A double-clamped beam 613.2.2. A cantilever beam 643.3. Concluding remarks 66Part 2. Topology Optimization for Maximizing the Fracture Resistance 67Chapter 4. Topology Optimization for Optimal Fracture Resistance of Quasi-brittle Composites 694.1. Phase field modeling of crack propagation 714.1.1. Phase field approximation of cracks 714.1.2. Thermodynamics of the phase field crack evolution 724.1.3. Weak forms of displacement and phase field problems 754.1.4. Finite element discretization 764.2. Topology optimization model for fracture resistance 784.2.1. Model definitions 784.2.2. Sensitivity analysis 804.2.3. Extended BESO method 854.3. Numerical examples 874.3.1. Design of a 2D reinforced plate with one pre-existing crack notch 884.3.2. Design of a 2D reinforced plate with two pre-existing crack notches 934.3.3. Design of a 2D reinforced plate with multiple pre-existing cracks 964.3.4. Design of a 3D reinforced plate with a single pre-existing crack notch surface 984.4. Concluding remarks 101Chapter 5. Topology Optimization for Optimal Fracture Resistance Taking into Account Interfacial Damage 1035.1. Phase field modeling of bulk crack and cohesive interfaces 1045.1.1. Regularized representation of a discontinuous field 1045.1.2. Energy functional 1065.1.3. Displacement and phase field problems 1085.1.4. Finite element discretization and numerical implementation 1115.2. Topology optimization method 1145.2.1. Model definitions 1145.2.2. Sensitivity analysis 1165.3. Numerical examples 1195.3.1. Design of a plate with one initial crack under traction 1205.3.2. Design of a plate without initial cracks for traction loads 1235.3.3. Design of a square plate without initial cracks in tensile loading 1255.3.4. Design of a plate with a single initial crack under three-point bending 1285.3.5. Design of a plate containing multiple inclusions 1305.4. Concluding remarks 133Chapter 6. Topology Optimization for Maximizing the Fracture Resistance of Periodic Composites 1356.1. Topology optimization model 1366.2. Numerical examples 1386.2.1. Design of a periodic composite under three-point bending 1386.2.2. Design of a periodic composite under non-symmetric three-point bending 1466.3. Concluding remarks 151Conclusion 153References 157Index 173. |
| Note |
Description based on print version record. |
| Subject |
Topology.
|
|
MATHEMATICS -- Geometry -- General.
|
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Da, Daicong. Topology optimization design of heterogeneous materials and structures. London : ISTE Limited ; Hoboken, New Jersey : John Wiley & Sons, Incorporated, 2020, c2019 172 pages 9781786305589 (DLC) 2019947662 |
| ISBN |
9781786305589 |
|
9781119687535 (e-book) |
|
