Multiscale Structural Topology Optimization

Multiscale Structural Topology Optimization

1st Edition - April 4, 2016

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  • Author: Liang Xia
  • eBook ISBN: 9780081011867
  • Hardcover ISBN: 9781785481000

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Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain.

Key Features

  • Presents the first attempts towards topology optimization design of nonlinear highly heterogeneous structures
  • Helps with simultaneous design of the topologies of both macroscopic structure and microscopic materials
  • Helps with development of computer codes for the designs of nonlinear structures and of materials with extreme constitutive properties
  • Focuses on the simultaneous design of both macroscopic structure and microscopic materials
  • Includes a reduce database model from a set of numerical experiments in the space of effective strain


Advanced students, researchers and professional engineers in mathematics for engineering, optimization and computational intelligence and computational methods in civil and structural engineering.

Table of Contents

    • Introduction
      • I.1 Background and motivations
      • I.2 Literature review on related subjects
      • I.3 Outline of the book
    • 1: Topology Optimization Framework for Multiscale Nonlinear Structures
      • Abstract:
      • 1.1 FE2 method
      • 1.2 Periodic boundary conditions
      • 1.3 Finite element discretization
      • 1.4 Topology optimization model
      • 1.5 Multiscale design framework
      • 1.6 Numerical examples
      • 1.7 Concluding remarks
    • 2: POD-based Adaptive Surrogate for the Design of Multiscale Structures
      • Abstract:
      • 2.1 Multiscale design framework
      • 2.2 POD-based adaptive surrogate
      • 2.3 Numerical examples
      • 2.4 Concluding remarks
    • 3: Topology Optimization of Multiscale Elastoviscoplastic Structures
      • Abstract:
      • 3.1 Topology optimization model
      • 3.2 Microscopic modeling
      • 3.3 Numerical examples
      • 3.4 Concluding remarks
    • 4: Simultaneous Topology Optimization of Structure and Materials
      • Abstract:
      • 4.1 Problem statement and decomposition
      • 4.2 Initial stiffness NR solution scheme
      • 4.3 Topology optimization models
      • 4.4 Numerical examples
      • 4.5 Concluding remarks
    • 5: Reduced Database Model for Material Microstructure Optimizations
      • Abstract:
      • 5.1 Simultaneous design framework
      • 5.2 Generalized material constitutive behavior
      • 5.3 Reduced database model (NEXP)
      • 5.4 Structural topology optimization
      • 5.5 General design algorithm
      • 5.6 Numerical examples
      • 5.7 Concluding remarks
    • Conclusion and Perspectives
    • Appendix: Design of Extreme Materials in Matlab
      • A.1 Introduction
      • A.2 Homogenization
      • A.3 Periodic boundary conditions
      • A.4 Optimization model
      • A.5 Matlab implementation
      • A.6 Illustrative examples
      • A.7 Concluding remarks
      • A.8 Matlab Code “topX.m”
    • Bibliography
    • Index

Product details

  • No. of pages: 184
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2016
  • Published: April 4, 2016
  • Imprint: ISTE Press - Elsevier
  • eBook ISBN: 9780081011867
  • Hardcover ISBN: 9781785481000

About the Author

Liang Xia

Liang Xia is a postdoctoral researcher in computational mechanics at the Laboratory of Multiscale Modelling and Simulation, University of Paris-Est, France. His research interests cover structural topology optimization, multiscale modeling and model order reduction. He is the author and co-author of 17 peer reviewed journal papers.

Affiliations and Expertise

Postdoctoral Researcher, Laboratory of Multiscale Modelling and Simulation, University of Paris-Est, France

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