Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
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 multilevel, level-set method for optimizing eigenvalues in shape design problems
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
Fuzzy tolerance multilevel approach for structural topology optimization
Computers and Structures
An isoparametric approach to level set topology optimization using a body-fitted finite-element mesh
Computers and Structures
Stress-based topology optimization using an isoparametric level set method
Finite Elements in Analysis and Design
Robust topology optimisation of bi-modulus structures
Computer-Aided Design
A survey of structural and multidisciplinary continuum topology optimization: post 2000
Structural and Multidisciplinary Optimization
Hi-index | 0.00 |
This paper presents an alternative level set method for shape and topology optimization of continuum structures. An implicit free boundary representation model is established by embedding structural boundary into the zero level set of a higher-dimensional level set function. An explicit parameterization scheme for the level set surface is proposed by using radial basis functions with compact support. In doing so, the originally more difficult shape and topology optimization, driven by the temporal and spatial Hamilton-Jacobi partial differential equation (PDE), is transformed into a relatively easier size optimization of the expansion coefficients of the basis functions. The design optimization is converted to an iterative numerical process that combines the parameterization with a derivation of the shape sensitivity of the design functions, so as to allow using mathematical programming algorithms to solve the level set-based design problem and avoid directly solving the Hamilton-Jacobi PDE. Furthermore, a numerically more stable and efficient volume integration scheme is proposed to implement calculations of the shape derivatives, leading to the creation of new holes which are generated initially along the boundary and then propagated to the interior of the design domain. Two widely studied examples are used to demonstrate the effectiveness of the proposed optimization method.