Topology Optimization in Structural and Continuum Mechanics, 1st Edition

  • Published By:
  • ISBN-10: 3709116430
  • ISBN-13: 9783709116432
  • DDC: 530.15
  • Grade Level Range: College Freshman - College Senior
  • 471 Pages | eBook
  • Original Copyright 2014 | Published/Released June 2014
  • This publication's content originally published in print form: 2014

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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.

Table of Contents

Front Cover.
Other Frontmatter.
Half Title Page.
Title Page.
Copyright Page.
1: Structural Topology OptImIzatIon (STO) – Exact AnalytIcal SolutIons: Part I.
2: Structural Topology Optimization (STO) – Exact Analytical Solutions: Part II.
3: Some Fundamental Properties of Exact Optimal Structural Topologies.
4: Validation of Numerical Methods by Analytical Benchmarks, and Verification of Exact Solutions by Numerical Methods.
5: A Brief Review of Numerical Methods of Structural Topology Optimization.
6: On Basic Properties of Michell’s Structures.
7: Structural Shape and Topology Optimization.
8: Compliance Minimization of Two-Material Elastic Structures.
9: The Free Material Design in Linear Elasticity.
10: Introductory Notes on Topological Design Optimization of Vibrating Continuum Structures.
11: Structural Topology Optimization with Respect to Eigenfrequencies of Vibration.
12: On Optimum Design and Periodicity of Band-Gap Structures.
13: Topological Design for Minimum Dynamic Compliance of Structures under Forced Vibration.
14: Topological Design for Minimum Sound Emission from Structures under Forced Vibration.
15: Discrete Material Optimization of Vibrating Laminated Composite Plates for Minimum Sound Emission.
16: Topology Optimization of Diffusive Transport Problems.
17: Topology Optimization of Flows: Stokes and Navier-Stokes Models.
18: Topology Optimization of Coupled Multi-Physics Problems.
19: The Extended Finite Element Method.
20: Topology Optimization under Uncertainty.