Generating optimal topologies in structural design using a homogenization method
Computer Methods in Applied Mechanics and Engineering
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Fast reaction, slow diffusion, and curve shortening
SIAM Journal on Applied Mathematics
Front propagation and phase field theory
SIAM Journal on Control and Optimization
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
A continuum model of grain boundaries
Physica D
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
The Topological Asymptotic for PDE Systems: The Elasticity Case
SIAM Journal on Control and Optimization
Introduction to Shape Optimization: Theory, Approximation, and Computation
Introduction to Shape Optimization: Theory, Approximation, and Computation
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Sharp interface tracking using the phase-field equation
Journal of Computational Physics
Phase-Field Relaxation of Topology Optimization with Local Stress Constraints
SIAM Journal on Control and Optimization
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
Optimal topologies derived from a phase-field method
Structural and Multidisciplinary Optimization
Structural and Multidisciplinary Optimization
Phase field method to optimize dielectric devices for electromagnetic wave propagation
Journal of Computational Physics
Development of a novel phase-field method for local stress-based shape and topology optimization
Computers and Structures
Structural and Multidisciplinary Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
Topological nano-aperture configuration by structural optimization based on the phase field method
Structural and Multidisciplinary Optimization
Design methodology of piezoelectric energy-harvesting skin using topology optimization
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
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This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.