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Radial basis functions and level set method for structural topology optimization

https://doi.org/10.1002/nme.1536
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Evolutionary Structural Optimization
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Shape Optimization by the Homogenization Method
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Topology Optimization: Theory, Methods, and Applications
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Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions
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Topology and Generalized Layout Optimization of Elastic Structures
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Level Set Methods and Dynamic Implicit Surfaces
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A fast level set based algorithm for topology-independent shape modeling
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Optimal shape design as a material distribution problem
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Generalized shape optimization without homogenization
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Interpolation of scattered data: Distance matrices and conditionally positive definite functions
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Error estimates and condition numbers for radial basis function interpolation
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Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme
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Hierarchical optimization of material and structure
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Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics
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Stress ratio and compliance based methods in topology optimization – a critical review
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A 99 line topology optimization code written in Matlab
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Shape optimization by the homogenization method
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Material interpolation schemes in topology optimization
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Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation
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A fast algorithm for particle simulations
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Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
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Crystal growth and dendritic solidification
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Generating optimal topologies in structural design using a homogenization method
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A simple evolutionary procedure for structural optimization
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Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates
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Theory and applications of the multiquadric-biharmonic method 20 years of discovery 1968–1988
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A level-set based variational method for design and optimization of heterogeneous objects
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Structural topology design optimization using Genetic Algorithms with a bit-array representation
inferredcites →https://doi.org/10.1016/j.cma.2004.12.019openalex-snapshot
Eulerian shape design sensitivity analysis and optimization with a fixed grid
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Graph representation for structural topology optimization using genetic algorithms
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A volumetric integral radial basis function method for time-dependent partial differential equations. I. Formulation
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Structural optimization using sensitivity analysis and a level-set method
inferredcites →https://doi.org/10.1016/j.jcp.2003.09.033openalex-snapshot
Incorporating topological derivatives into level set methods
inferredcites →https://doi.org/10.1016/j.jcp.2003.11.010openalex-snapshot
Numerical methods for high dimensional Hamilton–Jacobi equations using radial basis functions
inferredcites →https://doi.org/10.1016/j.jcp.2004.04.011openalex-snapshot
Numerical approximations of singular source terms in differential equations
inferredcites →https://doi.org/10.1016/s0045-7825(00)00356-xopenalex-snapshot
Topology optimization using regularized intermediate density control
inferredcites →https://doi.org/10.1016/s0045-7825(01)00251-1openalex-snapshot
Design of multiphysics actuators using topology optimization – Part I: One-material structures
inferredcites →https://doi.org/10.1016/s0045-7825(02)00559-5openalex-snapshot
A level set method for structural topology optimization
inferredcites →https://doi.org/10.1016/s0045-7949(01)00012-8openalex-snapshot
Comparisons between algorithms for structural topology optimization using a series of benchmark studies
inferredcites →https://doi.org/10.1016/s0898-1221(03)90179-9openalex-snapshot
Level set methods and dynamic implicit surfaces
inferredcites →https://doi.org/10.1017/s0022112095003624openalex-snapshot
Dynamical behaviour of a premixed turbulent open V-flame
inferredcites →https://doi.org/10.1017/s0962492900000015openalex-snapshot
Radial basis functions
inferredcites →https://doi.org/10.1023/a:1013666503249openalex-snapshot
Compact Unstructured Representations for Evolutionary Design
inferredcites →https://doi.org/10.1023/a:1020822324006openalex-snapshot
A Self-Referencing Level-Set Method for Image Reconstruction from Sparse Fourier Samples
inferredcites →https://doi.org/10.1080/14786440409463229openalex-snapshot
LVIII. The limits of economy of material in frame-structures
inferredcites →https://doi.org/10.1090/s0025-5718-1982-0637296-4openalex-snapshot
Scattered data interpolation: tests of some methods
inferredcites →https://doi.org/10.1108/02644400510585493openalex-snapshot
Bar‐system representation for topology optimization using genetic algorithms
inferredcites →https://doi.org/10.1109/sma.2001.923379openalex-snapshot
Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions
inferredcites →https://doi.org/10.1115/1.1319158openalex-snapshot
Design of Structures and Compliant Mechanisms by Evolutionary Optimization of Morphological Representations of Topology
inferredcites →https://doi.org/10.1115/1.1480818openalex-snapshot
Design Synthesis of Path Generating Compliant Mechanisms by Evolutionary Optimization of Topology and Shape
inferredcites →https://doi.org/10.1116/1.1380230openalex-snapshot
Extension velocities for level set based surface profile evolution
inferredcites →https://doi.org/10.1137/0728049openalex-snapshot
High-Order Essentially Nonoscillatory Schemes for Hamilton–Jacobi Equations
inferredcites →https://doi.org/10.1137/s1064827596298245openalex-snapshot
An Efficient, Interface-Preserving Level Set Redistancing Algorithm and Its Application to Interfacial Incompressible Fluid Flow
inferredcites →https://doi.org/10.1137/s106482759732455xopenalex-snapshot
Weighted ENO Schemes for Hamilton--Jacobi Equations
inferredcites →https://doi.org/10.1145/1053205.1053207openalex-snapshot
The method of lines for the numerical solution of partial differential equations (abstract)
inferredcites →https://doi.org/10.1145/1198555.1198645openalex-snapshot
Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions
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Reconstruction and representation of 3D objects with radial basis functions
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The method of lines for the numerical solution of partial differential equations
inferredcites →https://doi.org/10.2307/2007474openalex-snapshot
Scattered Data Interpolation: Tests of Some Method
inferredcites →https://doi.org/10.2514/6.2004-4564openalex-snapshot
Incorporating Topological Derivatives into Level Set Methods for Structural Topology Optimization
inferredcites →https://doi.org/10.3970/cmes.2004.006.373openalex-snapshot
PDE-Driven Level Sets, Shape Sensitivity and Curvature Flow for Structural Topology Optimization
inferredcites →https://doi.org/10.5860/choice.35-5129openalex-snapshot
Advanced engineering mathematics

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Level set topology optimization for design‐dependent pressure load problems
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A velocity field level set method for shape and topology optimization
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Topology Optimization of Arc Unit Cells by Extending Energy‐Based Homogenization and Parametric Level Set Methods
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Multi‐Material Structural Topology Optimization via Dynamic Body‐Fitted Multi‐Trimmed Mesh Evolution and Reaction–Diffusion‐Based Level‐Set Method
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Concurrent topology optimization of multiple components sharing partial design domain based on distance regularized parameterized level set method
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Developing Mechanical Metamaterials Under an Adaptable Topology Optimization Design Framework
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Level-Set-Based Topology Optimization of a Geometrically Nonlinear Structure Considering Thermo-mechanical Coupling Effect
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An Integrated Bi-directional Computing Framework for Composite Design Based on Self-Consistent Clustering Analysis and Conditional Generative Adversarial Network (SCA-CGAN)
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Non-Probabilistic Interval Reliability-Based Topology Optimization Framework for Buckling-Constrained Structures Using Parametric Level Set Method
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Parameterized level set method for structural topology optimization based on the Cosserat elasticity
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A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization
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Phononic crystal design: maximizing and customizing bandgaps using parameterized level set method-based topology optimization
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Topology optimization in Bernoulli free boundary problems
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A 2D topology optimisation algorithm in NURBS framework with geometric constraints
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A novel discrete adjoint-based level set topology optimization method in B-spline space
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Inversion of impact-echo data using a shape optimization approach
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Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements
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Concurrent optimization of structural topology and infill properties with a CBF-based level set method
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A regularization scheme for explicit level-set XFEM topology optimization
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Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency
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Manufacturing cost constrained topology optimization for additive manufacturing
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Level set band method: A combination of density-based and level set methods for the topology optimization of continuums
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An M-VCUT level set-based data-driven model of microstructures and optimization of two-scale structures
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Minimum width control in topology optimization of lattice structure through a M-VCUT level set based substructure
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The shape optimization of the arterial graft design by level set methods
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Topology Optimization Methods for 3D Structural Problems: A Comparative Study
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Step-size adaptive parametric level set method for structural topology optimization
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MQ quasi-interpolation-based level set method for structural topology optimization
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Parameterized level set method based topology optimization of transient heat conduction structures
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A coupled meshless element-free Galerkin and radial basis functions method for level set-based topology optimization
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Structural topology optimization using an enhanced and robust genetic algorithm
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Introduction
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Feature-based modeling and sensitivity analysis for structural optimization
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Feature-driven optimization method and applications
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Development of level set methodologies for different geometric discontinuities
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From numerical optima to flight hardware: A review of topology optimization for space applications
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Stiffness and strength enhancement of triply periodic minimal surface-based shell lattices via a novel shape optimization framework
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A survey of manufacturing oriented topology optimization methods
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Topological shape optimization of 3D micro-structured materials using energy-based homogenization method
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Smooth geometry extraction from SIMP topology optimization: Signed distance function approach with volume preservation
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Reaction–diffusion level set: A B‑spline route to triply periodic minimal surfaces
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Radial basis functions and level set method for image segmentation using partial differential equation
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A modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials
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Marching cubes-based isogeometric topology optimization method with parametric level set
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A robust topology optimization method considering bounded field parameters with uncertainties based on the variable time step parametric level-set method
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A level-set-based topology optimization strategy using radial basis functions and a Hilbertian velocity extension
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The identification of voids and inclusions based on the parameter level set method using boundary data
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Level set-based topology optimization for thermal-fluid system based on the radial basis functions
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High-performance stress-constrained topology optimization using level set method with inexact adjoint sensitivities
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Parametric level-set dynamic topology optimization for reusable periodic motion of pneumatic soft robots
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Parametrized level set method for a coupled thermal–fluid problem using radial basis functions
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Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method
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Deposition path planning-integrated structural topology optimization for 3D additive manufacturing subject to self-support constraint
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Level set-based heterogeneous object modeling and optimization
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A Level Set Based Density Method for Optimizing Structures with Curved Grid Stiffeners
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Topology optimization using Gaussian
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A parametric level set based collage method for an inverse problem in elliptic partial differential equations
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A parametrized level set based topology optimization method for analysing thermal problems
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A transformed radial basis function collocation method improving robustness of shape parameters selection
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Topology optimization of modular structures with multiple assemblies and applications to airborne shelves
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A new level set method for systematic design of hinge-free compliant mechanisms
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A level set approach for optimal design of smart energy harvesters
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An implicit model for the integrated optimization of component layout and structure topology
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Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function
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Structural topology and shape optimization using a level set method with distance-suppression scheme
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A level set method for topological shape optimization of 3D structures with extrusion constraints
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A multi-material level set-based topology and shape optimization method
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Stress constrained topology optimization with free-form design domains
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Feature-driven topology optimization method with signed distance function
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Multiscale isogeometric topology optimization for lattice materials
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An isogeometrical approach to structural level set topology optimization
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Parametric structural shape & topology optimization with a variational distance-regularized level set method
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Topology optimization for concurrent design of structures with multi-patch microstructures by level sets
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Parameterized level-set based topology optimization method considering symmetry and pattern repetition constraints
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Integrated topology optimization of multi-component structures considering connecting interface behavior
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Stable hole nucleation in level set based topology optimization by using the material removal scheme of BESO
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Level set based shape optimization using trimmed hexahedral meshes
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A surrogate assisted adaptive framework for robust topology optimization
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Cellular level set in B-splines (CLIBS): A method for modeling and topology optimization of cellular structures
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Generalized hole nucleation through BESO for the level set based topology optimization of multi-material structures
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A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets
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Topology optimization using material-field series expansion and Kriging-based algorithm: An effective non-gradient method
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Simultaneous material, shape and topology optimization
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A parametric divergence-free vector field method for the optimization of composite structures with curvilinear fibers
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Reverse shape compensation via a gradient-based moving particle optimization method
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On tailoring fracture resistance of brittle structures: A level set interface-enriched topology optimization approach
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A parametric level set method for the optimization of composite structures with curvilinear fibers
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A parallel parameterized level set topology optimization framework for large-scale structures with unstructured meshes
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A reaction diffusion-based B-spline level set (RDBLS) method for structural topology optimization
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Concurrent optimization of topological configuration and continuous fiber path for composite structures — A unified level set approach
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A feature-driven robust topology optimization strategy considering movable non-design domain and complex uncertainty
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A level set driven concurrent reliability-based topology optimization (LS-CRBTO) strategy considering hybrid uncertainty inputs and damage defects updating
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A level set-based interface-enriched topology optimization for the design of phononic crystals with smooth boundaries
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A novel quasi-smooth tetrahedral numerical manifold method and its application in topology optimization based on parameterized level-set method
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A non-uniform rational B-splines (NURBS) based optimization method for fiber path design
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Strength-based collaborative topology optimization for continuous fiber reinforced composites
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A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set
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Concurrent topology optimization of two-scale structures with minimum width control in microscale by using a M-VCUT level set based model of microstructures
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A parallel parameterized level set method for large-scale structural topology optimization under design-dependent load
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A CPU-parallel thermal topology optimization framework for arbitrary structures using flood fill algorithm and implicit identification model
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RBF-parameterized level-set boundary modeling for accelerating CMA-ES-based topology optimization with box constraint handling
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A peridynamics-based topology optimization framework for enhancing dynamic fracture resistance
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Quasi-smooth manifold element-based parameterized level set method for microstructure design with energy homogenization
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Concurrent topology optimization of co-dimensional continuum structures within a unified level set field
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Robust topology optimization for thermal–fluid system under multi-source uncertainties using parametric level-set method and non-intrusive polynomial chaos expansion
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A two-stage multi-fidelity optimization procedure for honeycomb-type cellular materials
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Moving-boundary problems solved by adaptive radial basis functions
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Solving moving-boundary problems with the wavelet adaptive radial basis functions method
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Shape optimization for fluid flow with parametric level set method and deep neural networks
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Dynamic responses and mechanisms of 3D-printed continuous carbon fibre-reinforced meta-composites under different strain rates
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A review of structural topology optimization for fiber-reinforced composites
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Enhancing performance for additively manufactured optimal CFRP structures
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