### Abstract

A displacement-based optimization strategy is extended to the design of truss structures with geometric and material nonlinear responses. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal cross-sectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples, which include material and geometric nonlinearities, for which it appears to be efficient and robust.

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

Pages (from-to) | 214-221 |

Number of pages | 8 |

Journal | Structural and Multidisciplinary Optimization |

Volume | 23 |

Issue number | 3 |

DOIs | |

State | Published - Apr 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- Dual variables
- Geometric and material nonlinearities
- Linear programming
- Truss design
- Two-level optimization

### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Mechanics of Materials
- Computational Mechanics
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*Structural and Multidisciplinary Optimization*,

*23*(3), 214-221. https://doi.org/10.1007/s00158-002-0179-1

**Optimization of nonlinear trusses using a displacement-based approach.** / Missoum, Samy; Gürdal, Z.; Gu, W.

Research output: Contribution to journal › Article

*Structural and Multidisciplinary Optimization*, vol. 23, no. 3, pp. 214-221. https://doi.org/10.1007/s00158-002-0179-1

}

TY - JOUR

T1 - Optimization of nonlinear trusses using a displacement-based approach

AU - Missoum, Samy

AU - Gürdal, Z.

AU - Gu, W.

PY - 2002/4

Y1 - 2002/4

N2 - A displacement-based optimization strategy is extended to the design of truss structures with geometric and material nonlinear responses. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal cross-sectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples, which include material and geometric nonlinearities, for which it appears to be efficient and robust.

AB - A displacement-based optimization strategy is extended to the design of truss structures with geometric and material nonlinear responses. Unlike the traditional optimization approach that uses iterative finite element analyses to determine the structural response as the sizing variables are varied by the optimizer, the proposed method searches for an optimal solution by using the displacement degrees of freedom as design variables. Hence, the method is composed of two levels: an outer level problem where the optimal displacement field is searched using general nonlinear programming algorithms, and an inner problem where a set of optimal cross-sectional dimensions are computed for a given displacement field. For truss structures, the inner problem is a linear programming problem in terms of the sizing variables regardless of the nature of the governing equilibrium equations, which can be linear or nonlinear in displacements. The method has been applied to three test examples, which include material and geometric nonlinearities, for which it appears to be efficient and robust.

KW - Dual variables

KW - Geometric and material nonlinearities

KW - Linear programming

KW - Truss design

KW - Two-level optimization

UR - http://www.scopus.com/inward/record.url?scp=0036540227&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036540227&partnerID=8YFLogxK

U2 - 10.1007/s00158-002-0179-1

DO - 10.1007/s00158-002-0179-1

M3 - Article

AN - SCOPUS:0036540227

VL - 23

SP - 214

EP - 221

JO - Structural and Multidisciplinary Optimization

JF - Structural and Multidisciplinary Optimization

SN - 1615-147X

IS - 3

ER -