### Abstract

In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is represented in terms of implicit functions and generally (but not necessarily) use the Hamilton-Jacobi equation as the evolution equation. Another set of approaches are referred to as phase-field methods; which generally use a reaction-diffusion equation, such as the Allen-Cahn equation, for topology evolution. In this work, we exhaustively analyze four level-set methods and one phase-field method, which are representative of the literature. In order to evaluate performance, all the methods are implemented in MATLAB and studied using two-dimensional compliance minimization problems.

Original language | English (US) |
---|---|

Pages (from-to) | 685-710 |

Number of pages | 26 |

Journal | Structural and Multidisciplinary Optimization |

Volume | 48 |

Issue number | 4 |

DOIs | |

State | Published - Jul 3 2013 |

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### Keywords

- Allen-Cahn equation
- Compliance minimization
- Differential equation-driven methods
- Hamilton-Jacobi equation
- Level-set method
- Phase-field method

### ASJC Scopus subject areas

- Control and Systems Engineering
- Software
- Computer Science Applications
- Computer Graphics and Computer-Aided Design
- Control and Optimization

### Cite this

*Structural and Multidisciplinary Optimization*,

*48*(4), 685-710. https://doi.org/10.1007/s00158-013-0935-4

**A critical comparative assessment of differential equation-driven methods for structural topology optimization.** / Gain, Arun L.; Paulino, Glaucio.

Research output: Contribution to journal › Review article

*Structural and Multidisciplinary Optimization*, vol. 48, no. 4, pp. 685-710. https://doi.org/10.1007/s00158-013-0935-4

}

TY - JOUR

T1 - A critical comparative assessment of differential equation-driven methods for structural topology optimization

AU - Gain, Arun L.

AU - Paulino, Glaucio

PY - 2013/7/3

Y1 - 2013/7/3

N2 - In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is represented in terms of implicit functions and generally (but not necessarily) use the Hamilton-Jacobi equation as the evolution equation. Another set of approaches are referred to as phase-field methods; which generally use a reaction-diffusion equation, such as the Allen-Cahn equation, for topology evolution. In this work, we exhaustively analyze four level-set methods and one phase-field method, which are representative of the literature. In order to evaluate performance, all the methods are implemented in MATLAB and studied using two-dimensional compliance minimization problems.

AB - In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is represented in terms of implicit functions and generally (but not necessarily) use the Hamilton-Jacobi equation as the evolution equation. Another set of approaches are referred to as phase-field methods; which generally use a reaction-diffusion equation, such as the Allen-Cahn equation, for topology evolution. In this work, we exhaustively analyze four level-set methods and one phase-field method, which are representative of the literature. In order to evaluate performance, all the methods are implemented in MATLAB and studied using two-dimensional compliance minimization problems.

KW - Allen-Cahn equation

KW - Compliance minimization

KW - Differential equation-driven methods

KW - Hamilton-Jacobi equation

KW - Level-set method

KW - Phase-field method

UR - http://www.scopus.com/inward/record.url?scp=84885468336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84885468336&partnerID=8YFLogxK

U2 - 10.1007/s00158-013-0935-4

DO - 10.1007/s00158-013-0935-4

M3 - Review article

AN - SCOPUS:84885468336

VL - 48

SP - 685

EP - 710

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 4

ER -