Ebook: Topology Design of Structures

The efficient use of materials is of great importance, and the choice of the basic topology for the design of structures and mechanical elements is crucial for the performance of sizing of shape optimization.
This volume provides a comprehensive review of the state of the art in topology design, spanning fundamental mathematical, mechanical and implementation issues. Topology design of discrete structures involves large scale computational problems and the need to select structural elements from a discrete set of possibilities. The formulation and solution of discrete design problems are described, including new applications of genetic algorithms and dual methods. For continuum problems the emphasis is on the `homogenization method', which employs composite materials as the basis for defining shape in terms of material density, unifying macroscopic structural design optimization and micromechanics. All aspects of this field are covered, including computational aspects and the use of the homogenization method in a computer-aided design environment.

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Content:
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Fundamental Properties of Optimal Topologies....Pages 3-18
Topology Optimization of Three-Dimensional Trusses....Pages 19-30
Two Nonsmooth Approaches to Simultaneous Geometry and Topology Design of Trusses....Pages 31-42
Minimax Compliance Truss Topology Subject to Multiple Loading....Pages 43-54
An Interior Point Algorithm for Truss Topology Design....Pages 55-69
Truss Topology Optimization with Stress and Displacement Constraints....Pages 71-78
Front Matter....Pages 79-79
Discrete Valued Optimal Design Problems....Pages 81-88
Discrete Optimal Design Using a Genetic Algorithm....Pages 89-102
Lay-Out and Sizing Design of Civil Engineering Structures in Accordance with the Eurocodes....Pages 103-116
Genetic Algorithms in Structural Topology Optimization....Pages 117-133
Optimal Placement of Actuators and Other Peripherals for Large Space Structures....Pages 135-144
Passive/Active Strut Placement by Integer Programming....Pages 145-156
Front Matter....Pages 157-157
Topology and Generalized Layout Optimization of Elastic Structures....Pages 159-205
Topology Optimization and Optimal Shape Design Using Homogenization....Pages 207-218
A Displacement-Based Topology Design Method with Self-Adaptive Layered Materials....Pages 219-238
A Numerical Algorithm for Topology and Shape Optimization....Pages 239-248
Front Matter....Pages 249-249
Layout Theory for Grid-Type Structures....Pages 251-272
Topology Optimization Using Iterative Continuum-Type Optimality Criteria (COC) Methods for Discretized Systems....Pages 273-286
Some Explorations in the Genesis of Structures....Pages 287-300
Front Matter....Pages 301-301
Imbedding/Control Approach for Solving Optimal Shape Design Problems....Pages 303-306
Front Matter....Pages 301-301
Applications of Material Derivative Method....Pages 307-311
Optimal Design of Thin Laminated Composite Structures....Pages 313-327
Front Matter....Pages 329-329
Why does it seem difficult to avoid homogenization type methods in order to change topology in shape optimization....Pages 331-336
Existence Via Relaxation for Some Domain Optimization Problems....Pages 337-343
Extremal Eigenvalue Problems for Starlike Drums....Pages 345-352
Front Matter....Pages 353-353
On the Strength of Composite Materials: Variational Bounds and Computational Aspects....Pages 355-374
Effective Properties for Non-linear Composite Materials: Computational Aspects....Pages 375-394
The Warping and the Torsion Problems in a Quasi-Periodically Perforated Domain....Pages 395-404
Front Matter....Pages 405-405
Optimum Layout and Shape of Plate Structures Using Homogenization....Pages 407-420
Optimal Reliability Design of Plates....Pages 421-435
Topology Optimization of Linear Elastic Structures Subjected to Thermal Loads....Pages 437-450
Truss Topology Design for Elastic/Softening Materials....Pages 451-467
Decision Makings for Initial Designs Made of Advanced Materials....Pages 469-480
Front Matter....Pages 481-481
Integrating Topology and Boundary Variations Design Methods in a CAD System....Pages 483-499
Integrated Structural Optimization System....Pages 501-514
Front Matter....Pages 515-515
Topology Design of Discrete Structures....Pages 517-534
An Optimization-Based Approach to the Domain Decomposition Problem in Parallel Finite Element Analysis....Pages 535-546
Stability of Optimal Structures of Elastic Composites....Pages 547-558
Back Matter....Pages 559-569

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Content:
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Fundamental Properties of Optimal Topologies....Pages 3-18
Topology Optimization of Three-Dimensional Trusses....Pages 19-30
Two Nonsmooth Approaches to Simultaneous Geometry and Topology Design of Trusses....Pages 31-42
Minimax Compliance Truss Topology Subject to Multiple Loading....Pages 43-54
An Interior Point Algorithm for Truss Topology Design....Pages 55-69
Truss Topology Optimization with Stress and Displacement Constraints....Pages 71-78
Front Matter....Pages 79-79
Discrete Valued Optimal Design Problems....Pages 81-88
Discrete Optimal Design Using a Genetic Algorithm....Pages 89-102
Lay-Out and Sizing Design of Civil Engineering Structures in Accordance with the Eurocodes....Pages 103-116
Genetic Algorithms in Structural Topology Optimization....Pages 117-133
Optimal Placement of Actuators and Other Peripherals for Large Space Structures....Pages 135-144
Passive/Active Strut Placement by Integer Programming....Pages 145-156
Front Matter....Pages 157-157
Topology and Generalized Layout Optimization of Elastic Structures....Pages 159-205
Topology Optimization and Optimal Shape Design Using Homogenization....Pages 207-218
A Displacement-Based Topology Design Method with Self-Adaptive Layered Materials....Pages 219-238
A Numerical Algorithm for Topology and Shape Optimization....Pages 239-248
Front Matter....Pages 249-249
Layout Theory for Grid-Type Structures....Pages 251-272
Topology Optimization Using Iterative Continuum-Type Optimality Criteria (COC) Methods for Discretized Systems....Pages 273-286
Some Explorations in the Genesis of Structures....Pages 287-300
Front Matter....Pages 301-301
Imbedding/Control Approach for Solving Optimal Shape Design Problems....Pages 303-306
Front Matter....Pages 301-301
Applications of Material Derivative Method....Pages 307-311
Optimal Design of Thin Laminated Composite Structures....Pages 313-327
Front Matter....Pages 329-329
Why does it seem difficult to avoid homogenization type methods in order to change topology in shape optimization....Pages 331-336
Existence Via Relaxation for Some Domain Optimization Problems....Pages 337-343
Extremal Eigenvalue Problems for Starlike Drums....Pages 345-352
Front Matter....Pages 353-353
On the Strength of Composite Materials: Variational Bounds and Computational Aspects....Pages 355-374
Effective Properties for Non-linear Composite Materials: Computational Aspects....Pages 375-394
The Warping and the Torsion Problems in a Quasi-Periodically Perforated Domain....Pages 395-404
Front Matter....Pages 405-405
Optimum Layout and Shape of Plate Structures Using Homogenization....Pages 407-420
Optimal Reliability Design of Plates....Pages 421-435
Topology Optimization of Linear Elastic Structures Subjected to Thermal Loads....Pages 437-450
Truss Topology Design for Elastic/Softening Materials....Pages 451-467
Decision Makings for Initial Designs Made of Advanced Materials....Pages 469-480
Front Matter....Pages 481-481
Integrating Topology and Boundary Variations Design Methods in a CAD System....Pages 483-499
Integrated Structural Optimization System....Pages 501-514
Front Matter....Pages 515-515
Topology Design of Discrete Structures....Pages 517-534
An Optimization-Based Approach to the Domain Decomposition Problem in Parallel Finite Element Analysis....Pages 535-546
Stability of Optimal Structures of Elastic Composites....Pages 547-558
Back Matter....Pages 559-569
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