Level set based method for simultaneous optimization of material property and topology of functionally graded structures

Authors:
Qi Xia;Michael Y. Wang
Affiliations:
The Chinese University of Hong Kong;The Chinese University of Hong Kong
Venue:
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Year:
2007

Citing 16
Cited 0

Efficient implementation of essentially non-oscillatory shock-capturing schemes

Journal of Computational Physics
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
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations

SIAM Journal on Numerical Analysis
Real functions for representation of rigid solids

Computer Aided Geometric Design
Variational methods in image segmentation

Variational methods in image segmentation
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)

Journal of Computational Physics
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
Reconstruction and representation of 3D objects with radial basis functions

Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Level set methods for optimization problems involving geometry and constraints I. Frequencies of a two-density inhomogeneous drum

Journal of Computational Physics
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

International Journal of Computer Vision
Interpolating Implicit Surfaces from Scattered Surface Data Using Compactly Supported Radial Basis Functions

SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Structural optimization using sensitivity analysis and a level-set method

Journal of Computational Physics
Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation, and magnification

IEEE Transactions on Image Processing

Quantified Score

Hi-index	0.00

Visualization

Abstract

A level set based method is proposed for simultaneous optimization of material property and topology of functionally graded structures. The objective is to determine the optimal material property (via material volume fraction) and structural topology to maximize the performance of the structure in a given application. In the proposed method volume fraction and structural boundary are considered as design variables, with the former being discretized as a scaler field and the latter being implicitly represented by level set method. To perform simultaneous optimization, the two design variables are integrated into a common objective functional. Sensitivity analysis is conducted to obtain the descent directions. The optimization process is then expressed as the solution to a coupled Hamilton-Jacobi equation and diffusion partial differential equation. Numerical results are provided for the problem of mean compliance optimization in two dimensions.