The Feature-Driven Method for Structural Optimization

The Feature-Driven Method for Structural Optimization

1st Edition - November 5, 2020

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  • Authors: Weihong Zhang, Ying Zhou
  • eBook ISBN: 9780128213315
  • Paperback ISBN: 9780128213308

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The Feature-Driven Method for Structural Optimization details a novel structural optimization method within a CAD framework, integrating structural optimization and feature-based design. The book presents cutting-edge research on advanced structures and introduces the feature-driven structural optimization method by regarding engineering features as basic design primitives. Consequently, it presents a method that allows structural optimization and feature design to be done simultaneously so that feature attributes are preserved throughout the design process. The book illustrates and supports the effectiveness of the method described, showing potential applications through numerical modeling techniques and programming. This volume presents a high-performance optimization method adapted to engineering structures—a novel perspective that will help engineers in the computation, modeling and design of advanced structures.

Key Features

  • Integrates two independent methods - structural optimization and feature-based design—into one framework
  • Adapts the high performance optimization method to the practice of designing engineering structures
  • Provides numerical evidence for the effectiveness and potential of the methods described
  • Works within a computer-aided design framework to develop a novel structural optimization methodology
  • Presents engineering features as the basic design primitives in structural optimization


Engineers involved in structural design and optimization; Researchers and professional engineers in mathematics for engineering, optimization, computational intelligence and computational methods in civil and structural engineering

Table of Contents

  • Chapter 1. Introduction
    Chapter 2. Level-set functions and parametric functions
    2.1. Definitions of level-set function and parametric function
    2.1.1. Basic notions and geometric interpretations
    2.1.2. Gradient, curvature and convexity
    2.2. Heaviside function, dirac delta function and regularized forms
    2.2.1. Basic notions
    2.2.2. Regularized Heaviside function and dirac delta function
    2.3. Typical level-set functions
    2.3.1. Signed distance function and first-order approximation
    2.3.2. Radial basis function and properties
    2.3.3. Closed B-splines
    2.4. Relationship between implicit and parametric functions
    2.4.1. Transformation between implicit and parametric functions
    2.4.2. Parametric function for point-in-polygon test
    Chapter 3. Basis operations of level-set functions
    3.1. Operations of single level-set function
    3.1.1. Translation, rotation and scaling of a feature represented by level-set function
    3.1.2. Twisting, sweeping and polynomial operations of a feature
    3.2. Operations of multiple level-set functions
    3.2.1. Blending operation
    3.2.2. Boolean operations of features
    3.2.3. Boolean operations of features with max and min functions
    3.3. Typical max and min functions
    3.3.1. R-function
    3.3.2. Ricci function
    3.3.3. KS function
    3.3.4. Step function
    3.3.5. Examples of modelling 2D and 3D mechanical parts
    Chapter 4.  Structural analysis by B-spline finite cell method
    4.1. Introduction to B-spline finite cell method
    4.1.1. B-spline basis function
    4.1.2. Basic theory of B-spline finite cell method
    4.1.3. Cell refinement with quadtree/octree scheme
    4.2. Imposition of Dirichlet boundary condition with web method
    4.2.1. Imposition methods of Dirichlet boundary condition
    4.2.2. Weighted B-spline FCM for the imposition of Dirichlet boundary condition
    4.2.3. Formulations of weighting function and boundary value function
    4.3. Numerical examples
    4.3.1. Plate of infinite length with a circular hole
    4.3.2. A cylindrical sector subjected to harmonic Dirichlet boundary condition
    4.3.3. A cylinder subjected to prescribed radial displacement and temperature
    4.3.4. Thermo-elastic stress analysis of a heat exchanging device with prescribed temperature
    Chapter 5. Feature-based modelling and sensitivity analysis for topology optimization
    5.1. Feature-based modelling with level-set function
    5.1.1. Freeform design domain modeller (FDDM)
    5.1.2. Topology variation modeller (TVM)
    5.1.3. Action of the TVM onto the FDDM
    5.2. Problem statement of feature-driven optimization
    5.2.1. Formulations of feature-driven optimization problems
    5.2.2. Numerical treatments of active stress constraints
    5.3. Feature-based sensitivity analysis with level-set functions
    5.3.1. Sensitivity analysis with domain integral scheme
    5.3.2. Sensitivity analysis with boundary integral scheme
    5.3.3. Sensitivity property with design domain preserving
    5.3.4. Hamilton-Jacobi equation for the unification of implicit and parametric formulations
    5.4. Numerical examples
    5.4.1. Effect of FCM order on sensitivity accuracy with boundary integral scheme
    5.4.2. Effects of band-width on sensitivity accuracy with domain integral scheme
    Chapter 6.  Feature-driven optimization method and applications
    6.1. Unification of implicit and parametric shape optimization
    6.1.1. Implicit shape optimization with level-set functions
    6.1.2. Unified shape optimization with parametric functions and fixed mesh
    6.2. Shape optimization of Dirichlet and free boundaries
    6.2.1. Shape optimization of Dirichlet boundary
    6.2.2. Simultaneous shape optimization with parametric functions and fixed mesh
    6.3. Topology optimization of regular design domain structures
    6.3.1. RBF-based topology optimization of regular design domain structures
    6.3.2. Feature-driven topology optimization of regular design domain structures
    6.3.3. CBS-based topology optimization of regular design domain structures
    6.4. Topology optimization of freeform design domain structures
    6.4.1. RBF-based topology optimization of freeform design domain structures
    6.4.2. Feature-driven topology optimization of freeform design domain structures
    6.4.3. CBS-based topology optimization of regular freeform domain structures
    Chapter 7. Advanced applications of feature-driven optimization in problems including design-dependent loads
    7.1. Topology optimization including design-dependent body loads
    7.1.1. CBS-based model for topology optimization
    7.1.2. Sensitivity analysis of CBS-based model including design-dependent body loads
    7.1.3. Numerical examples including design-dependent body loads
    7.2. Concurrent shape and topology optimization involving design-dependent pressure loads
    7.2.1. CBS-based model for concurrent shape and topology optimization
    7.2.2. Sensitivity analysis of design-dependent pressure loads
    7.2.3. Numerical examples including design-dependent pressure loads
    Chapter 8. Advanced applications of feature-driven optimization for additive manufacturing
    8.1. Topology optimization of self-support structure with polygon features
    8.1.1. Representation of polygon-featured holes
    8.1.2. Construction of the level-set function for a polygon-featured hole with Boolean operations
    8.1.3. Elimination of unprintable V-shaped areas caused by intersecting polygon-featured holes
    8.1.4. Numerical examples
    8.2. Topology optimization with enclosed voids restriction
    8.2.1. Side constraint scheme for structural connectivity
    8.2.2. Numerical examples

Product details

  • No. of pages: 350
  • Language: English
  • Copyright: © Elsevier 2020
  • Published: November 5, 2020
  • Imprint: Elsevier
  • eBook ISBN: 9780128213315
  • Paperback ISBN: 9780128213308

About the Authors

Weihong Zhang

Prof. Weihong Zhang obtained his PhD in University of Liège, Belgium. He is currently Vice-President of Northwestern Polytechnical University, Cheung Kong Chair Professor and Distinguished Young Scholar of National Natural Science Foundation of China. His research interests cover Computational Mechanics of Solids and Structures, Optimal Designs of Advanced Materials, Structures and Advanced Manufacturing Process.

Affiliations and Expertise

Vice-President of Northwestern Polytechnical University, Cheung Kong and Chair Professor and Distinguished Young Scholar, National Natural Science Foundation, China

Ying Zhou

Researcher at Northwestern Polytechnical University in China. Her research focuses on innovative topology optimization methods, and feature-driven methods for structural optimization. She has published nine papers on computational mechanics and structural optimization

Affiliations and Expertise

Researcher, Northwestern Polytechnical University, Xi'an, China

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