The Feature-Driven Method for Structural Optimization

Chapter 1. IntroductionChapter 2. Level-set functions and parametric functions2.1. Definitions of level-set function and parametric function2.1.1. Basic notions and geometric interpretations2.1.2. Gradient, curvature and convexity2.2. Heaviside function, dirac delta function and regularized forms2.2.1. Basic notions2.2.2. Regularized Heaviside function and dirac delta function2.3. Typical level-set functions2.3.1. Signed distance function and first-order approximation2.3.2. Radial basis function and properties2.3.3. Closed B-splines2.4. Relationship between implicit and parametric functions2.4.1. Transformation between implicit and parametric functions2.4.2. Parametric function for point-in-polygon testChapter 3. Basis operations of level-set functions3.1. Operations of single level-set function3.1.1. Translation, rotation and scaling of a feature represented by level-set function3.1.2. Twisting, sweeping and polynomial operations of a feature3.2. Operations of multiple level-set functions3.2.1. Blending operation3.2.2. Boolean operations of features3.2.3. Boolean operations of features with max and min functions3.3. Typical max and min functions3.3.1. R-function3.3.2. Ricci function3.3.3. KS function3.3.4. Step function3.3.5. Examples of modelling 2D and 3D mechanical partsChapter 4. Structural analysis by B-spline finite cell method4.1. Introduction to B-spline finite cell method4.1.1. B-spline basis function4.1.2. Basic theory of B-spline finite cell method4.1.3. Cell refinement with quadtree/octree scheme4.2. Imposition of Dirichlet boundary condition with web method4.2.1. Imposition methods of Dirichlet boundary condition4.2.2. Weighted B-spline FCM for the imposition of Dirichlet boundary condition4.2.3. Formulations of weighting function and boundary value function4.3. Numerical examples4.3.1. Plate of infinite length with a circular hole4.3.2. A cylindrical sector subjected to harmonic Dirichlet boundary condition4.3.3. A cylinder subjected to prescribed radial displacement and temperature4.3.4. Thermo-elastic stress analysis of a heat exchanging device with prescribed temperatureChapter 5. Feature-based modelling and sensitivity analysis for topology optimization5.1. Feature-based modelling with level-set function5.1.1. Freeform design domain modeller (FDDM)5.1.2. Topology variation modeller (TVM)5.1.3. Action of the TVM onto the FDDM5.2. Problem statement of feature-driven optimization5.2.1. Formulations of feature-driven optimization problems5.2.2. Numerical treatments of active stress constraints5.3. Feature-based sensitivity analysis with level-set functions5.3.1. Sensitivity analysis with domain integral scheme5.3.2. Sensitivity analysis with boundary integral scheme5.3.3. Sensitivity property with design domain preserving5.3.4. Hamilton-Jacobi equation for the unification of implicit and parametric formulations5.4. Numerical examples5.4.1. Effect of FCM order on sensitivity accuracy with boundary integral scheme5.4.2. Effects of band-width on sensitivity accuracy with domain integral schemeChapter 6. Feature-driven optimization method and applications6.1. Unification of implicit and parametric shape optimization6.1.1. Implicit shape optimization with level-set functions6.1.2. Unified shape optimization with parametric functions and fixed mesh 6.2. Shape optimization of Dirichlet and free boundaries6.2.1. Shape optimization of Dirichlet boundary6.2.2. Simultaneous shape optimization with parametric functions and fixed mesh6.3. Topology optimization of regular design domain structures6.3.1. RBF-based topology optimization of regular design domain structures6.3.2. Feature-driven topology optimization of regular design domain structures6.3.3. CBS-based topology optimization of regular design domain structures6.4. Topology optimization of freeform design domain structures 6.4.1. RBF-based topology optimization of freeform design domain structures6.4.2. Feature-driven topology optimization of freeform design domain structures6.4.3. CBS-based topology optimization of regular freeform domain structuresChapter 7. Advanced applications of feature-driven optimization in problems including design-dependent loads7.1. Topology optimization including design-dependent body loads7.1.1. CBS-based model for topology optimization7.1.2. Sensitivity analysis of CBS-based model including design-dependent body loads7.1.3. Numerical examples including design-dependent body loads7.2. Concurrent shape and topology optimization involving design-dependent pressure loads7.2.1. CBS-based model for concurrent shape and topology optimization7.2.2. Sensitivity analysis of design-dependent pressure loads7.2.3. Numerical examples including design-dependent pressure loadsChapter 8. Advanced applications of feature-driven optimization for additive manufacturing8.1. Topology optimization of self-support structure with polygon features8.1.1. Representation of polygon-featured holes8.1.2. Construction of the level-set function for a polygon-featured hole with Boolean operations8.1.3. Elimination of unprintable V-shaped areas caused by intersecting polygon-featured holes8.1.4. Numerical examples8.2. Topology optimization with enclosed voids restriction8.2.1. Side constraint scheme for structural connectivity8.2.2. Numerical examples