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
Error estimates for interpolation by compactly supported radial basis functions of minimal degree
Journal of Approximation Theory
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
SIAM Journal on Scientific Computing
A PDE-based fast local level set method
Journal of Computational Physics
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Level set methods: an overview and some recent results
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Optimization
Inverse and saturation theorems for radial basis function interpolation
Mathematics of Computation
Design of Compliant Mechanisms: Applications to MEMS
Analog Integrated Circuits and Signal Processing
Radial Basis Functions
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
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
A multilevel, level-set method for optimizing eigenvalues in shape design problems
Journal of Computational Physics
An extended level set method for shape and topology optimization
Journal of Computational Physics
A semi-implicit level set method for structural shape and topology optimization
Journal of Computational Physics
Design of piezoelectric actuators using a multiphase level set method of piecewise constants
Journal of Computational Physics
Journal of Computational Physics
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Medial zones: Formulation and applications
Computer-Aided Design
Phase field method to optimize dielectric devices for electromagnetic wave propagation
Journal of Computational Physics
Structural and Multidisciplinary Optimization
Level-set methods for structural topology optimization: a review
Structural and Multidisciplinary Optimization
Numerical instabilities in level set topology optimization with the extended finite element method
Structural and Multidisciplinary Optimization
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
Hi-index | 31.47 |
In this paper, a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms. The structural shape boundary is implicitly embedded into a higher-dimensional scalar function as its zero level set, resultantly, establishing the level set model. By applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function, the temporal and spatial Hamilton-Jacobi equation from the conventional level set method is then discretized into a series of algebraic equations. Accordingly, the original shape and topology optimization is now fully transformed into a parameterization problem, namely, size optimization with the expansion coefficients of interpolants as a limited number of design variables. Design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints. The structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method. It is highlighted that the present method can not only inherit the merits of the implicit boundary representation, but also avoid some unfavorable features of the conventional discrete level set method, such as the CFL condition restriction, the re-initialization procedure and the velocity extension algorithm. Finally, an extensively investigated example is presented to demonstrate the benefits and advantages of the present method, especially, its capability of creating new holes inside the design domain.