Topology Optimization in Structural and Continuum Mechanics

1. Front Matter

   Pages i-x

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2. Structural Topology Optimization (STO) – Exact Analytical Solutions: Part I

   • George I. N. Rozvany

   Pages 1-14

3. Structural Topology Optimization (STO) – Exact Analytical Solutions: Part II

   • George I. N. Rozvany, Erika Pinter

   Pages 15-34

4. Some Fundamental Properties of Exact Optimal Structural Topologies

   • George I. N. Rozvany

   Pages 35-52

5. Validation of Numerical Methods by Analytical Benchmarks, and Verification of Exact Solutions by Numerical Methods

   • George I. N. Rozvany, Tomasz Sokół

   Pages 53-69

6. A Brief Review of Numerical Methods of Structural Topology Optimization

   • George I. N. Rozvany

   Pages 71-86

7. On Basic Properties of Michell’s Structures

   • Tomasz Lewiński, Tomasz Sokół

   Pages 87-128

8. Structural Shape and Topology Optimization

   • François Jouve

   Pages 129-173

9. Compliance Minimization of Two-Material Elastic Structures

   • Grzegorz Dzierżanowski, Tomasz Lewiński

   Pages 175-212

10. The Free Material Design in Linear Elasticity

    • Sławomir Czarnecki, Tomasz Lewiński

    Pages 213-257

11. Introductory Notes on Topological Design Optimization of Vibrating Continuum Structures

    • Niels Olhoff, Jianbin Du

    Pages 259-273

12. Structural Topology Optimization with Respect to Eigenfrequencies of Vibration

    • Niels Olhoff, Jianbin Du

    Pages 275-297

13. On Optimum Design and Periodicity of Band-gap Structures

    • Niels Olhoff, Bin Niu

    Pages 299-324

14. Topological Design for Minimum Dynamic Compliance of Structures under Forced Vibration

    • Niels Olhoff, Jianbin Du

    Pages 325-339

15. Topological Design for Minimum Sound Emission from Structures under Forced Vibration

    • Niels Olhoff, Jianbin Du

    Pages 341-357

16. Discrete Material Optimization of Vibrating Laminated Composite Plates for Minimum Sound Emission

    • Niels Olhoff, Bin Niu

    Pages 359-387

17. Topology Optimization of Diffusive Transport Problems

    • Kurt Maute

    Pages 389-407

18. Topology Optimization of Flows: Stokes and Navier-Stokes Models

    • Kurt Maute

    Pages 409-419

19. Topology Optimization of Coupled Multi-Physics Problems

    • Kurt Maute

    Pages 421-437

20. The Extended Finite Element Method

    • Kurt Maute

    Pages 439-456

The book covers new developments in structural topology optimization. Basic features and limitations of Michell’s truss theory, its extension to a broader class of support conditions, generalizations of truss topology optimization, and Michell continua are reviewed. For elastic bodies, the layout problems in linear elasticity are discussed and the method of relaxation by homogenization is outlined. The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case. For structures subjected to dynamic loads, it is explained how they can be designed so that the structural eigenfrequencies of vibration are as far away as possible from a prescribed external excitation frequency (or a band of excitation frequencies) in order to avoid resonance phenomena with high vibration and noise levels. For diffusive and convective transport processes and multiphysics problems, applications of the density method are discussed. In order to take uncertainty in material parameters, geometry, and operating conditions into account, techniques of reliability-based design optimization are introduced and reviewed for their applicability to topology optimization.

• Continuum Mechanics
• Fluid-structure Interaction
• Structural Design
• Structural Mechanics
• Topology Optimization

• Budapest University of Technology and Economics, Budapest, Hungary

  George I. N. Rozvany

• Warsaw University of Technology, Warsaw, Poland

  Tomasz Lewiński

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