Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Journal of Computational Physics
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
On Numerical Solution of Shape Inverse Problems
Computational Optimization and Applications
Optimality Conditions for Simultaneous Topology and Shape Optimization
SIAM Journal on Control and Optimization
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
A feature-based topological optimization for structure design
Advances in Engineering Software
Spatial to kinematically determined structural transformations
Advanced Engineering Informatics
Advances in Engineering Software
A hybrid topology optimization methodology combining simulated annealing and SIMP
Computers and Structures
Topology design of three-dimensional continuum structures using isosurfaces
Advances in Engineering Software
A level set solution to the stress-based structural shape and topology optimization
Computers and Structures
Topology optimization considering static failure theories for ductile and brittle materials
Computers and Structures
An automated stabilisation method for spatial to structural design transformations
Advanced Engineering Informatics
A method for shape and topology optimization of truss-like structure
Structural and Multidisciplinary Optimization
A Sequential Element Rejection and Admission (SERA) method for compliant mechanisms design
Structural and Multidisciplinary Optimization
Automated design studies: Topology versus One-Step Evolutionary Structural Optimisation
Advanced Engineering Informatics
Development of a novel phase-field method for local stress-based shape and topology optimization
Computers and Structures
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
Finite Elements in Analysis and Design
Structural and Multidisciplinary Optimization
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The level set method for structural topology optimization has been proposed and studied recently, which is basically a steepest descent method by combining the shape sensitivity analysis with the Hamilton-Jacobi equation for moving the level-set function, for doing topology design of structures. The paper considers the multi-material and multi-constraint problems, and investigates the topology optimization algorithm by using the different material representation models, and broadens its application from stiff structure designs and compliant mechanism designs to material designs by a number of benchmark examples. Meanwhile in order to further improve computational efficiency and overcome the difficulty that the level set method cannot generate new material interfaces during the optimization process, the multi-material topological derivative analysis is incorporated into the level set method for topological optimization.