目錄
Chapter 1 Introduction
1.1 Overview and motivation
1.2 Feature-based modeling and design in CAD
1.3 Feature-driven structural optimization
1.4 Layout of the book
References
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
2.3.3 Implicit B-spline
2.4 Relationship between implicit and parametric functions
2.4.1 Transformation between implicit and parametric functions
2.4.2 Parametric function for the point-in-polygon test
References
Chapter 3 Basic operations of level-set functions
3.1 Operations of a single level-set function
3.1.1 Translation, rotation, and scaling operations
3.1.2 Twisting, sweeping, and polynomial operations
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
3.4 Examples of modeling 2 - D and 3 - D mechanical parts
References
Chapter 4 B-spline finite cell method fur structural analysis
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 the Dirichlet boundary condition with the Web method
4.2.1 Imposition methods of the Dirichlet boundary condition
4.2.2 Weighted B-spline finite cell method
4.2.3 Formulations of the weighting function and the boundary value function
4.3 Numerical examples
4.3.1 Infinite plate with a circular hole
4.3.2 A cylindrical sector subject to harmonic Dirichlet boundary conditions
4.3.3 A cylinder subject to prescribed radial displacement and temperature
4.3.4 Thermoelastic stress analysis of a heat exchanging device with prescribed temperature
References
Chapter5 Feature-based modeling and sensitivity analysis for structural optimization
5.1 Feature-based modeling with level-set functions
5.1.1 Freeform design domain modeler
5.1.2 Topology variation modeler
5.1.3 Action of the TVM onto the FDDM
5.2 Problem statement of feature-driven optimization
5.2.1 Mathematical formulations
5.2.2 Numerical treatments of active stress constraints
5.3 Feature-based sensitivity analysis
5.3.1 Sensitivity analysis with the 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
References
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 the Dirichlet and free boundaries
6.2.1 Shape optimization of the Dirichlet boundary
6.2.2 Simultaneous shape optimization of free and Dirichlet boundaries
6.3 Topology optimization of the regular design domain
6.3.1 RBF-based topology optimization
6.3.2 Feature-driven topology optimization
6.3.3 CBS-based topology optimization
6.4 Topology optimization of the freeform design domain
6.4.1 RBF-based topology optimization
6.4.2 Feature-driven topology optimization
6.4.3 CBS-based topology optimization
References
Chapter 7 Feature-driven optimization for structures under 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 the 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 Implicit B-spline-based model for concurrent shape and topology optimization
7.2.2 Sensitivity analysis of implicit B-spline-based model involving design-dependent pressure loads
7.2.3 Numerical examples including design--dependent pressure loads
References
Chapter 8 Integration of feature-driven optimization with additive manufacturing
8.1 Topology optimization of self-supporting structure with polygon features
8.1.1 Representation of polygon-featured holes
8.1.2 Construction of the level-set function for a pol
References
Index
[