### Abstract

Many engineering systems are too complex to be defined in precise mathematical terms. They often contain information and features that are vague, imprecise, qualitative, linguistic or incomplete. The traditional deterministic and probabilistic techniques are not adequate to analyze such systems. This paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems. The development of the methodology starts from the basic concepts of fuzzy numbers and fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation, manipulation and solution of the finite element equations. Simple stress analysis problems involving vaguely defined geometry, material properties, external loads and boundary conditions are solved to establish and to illustrate the new procedure. The approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information. If complete data are known, the method handles the information similar to that of a probabilistic approach. The present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures.

Original language | English (US) |
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Title of host publication | Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference |

Publisher | AIAA |

Pages | 2519-2529 |

Number of pages | 11 |

Volume | 4 |

State | Published - 1996 |

Externally published | Yes |

Event | Proceedings of the 1996 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Part 4 (of 4) - Salt Lake City, UT, USA Duration: Apr 15 1996 → Apr 17 1996 |

### Other

Other | Proceedings of the 1996 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Part 4 (of 4) |
---|---|

City | Salt Lake City, UT, USA |

Period | 4/15/96 → 4/17/96 |

### Fingerprint

### ASJC Scopus subject areas

- Architecture

### Cite this

*Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference*(Vol. 4, pp. 2519-2529). AIAA.

**Fuzzy finite element approach for the analysis of imprecisely-defined systems.** / Rao, Singiresu S; Sawyer, James P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.*vol. 4, AIAA, pp. 2519-2529, Proceedings of the 1996 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Part 4 (of 4), Salt Lake City, UT, USA, 4/15/96.

}

TY - GEN

T1 - Fuzzy finite element approach for the analysis of imprecisely-defined systems

AU - Rao, Singiresu S

AU - Sawyer, James P.

PY - 1996

Y1 - 1996

N2 - Many engineering systems are too complex to be defined in precise mathematical terms. They often contain information and features that are vague, imprecise, qualitative, linguistic or incomplete. The traditional deterministic and probabilistic techniques are not adequate to analyze such systems. This paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems. The development of the methodology starts from the basic concepts of fuzzy numbers and fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation, manipulation and solution of the finite element equations. Simple stress analysis problems involving vaguely defined geometry, material properties, external loads and boundary conditions are solved to establish and to illustrate the new procedure. The approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information. If complete data are known, the method handles the information similar to that of a probabilistic approach. The present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures.

AB - Many engineering systems are too complex to be defined in precise mathematical terms. They often contain information and features that are vague, imprecise, qualitative, linguistic or incomplete. The traditional deterministic and probabilistic techniques are not adequate to analyze such systems. This paper aims at developing a fuzzy finite element approach for the analysis of imprecisely defined systems. The development of the methodology starts from the basic concepts of fuzzy numbers and fuzzy arithmetic and implements suitably defined fuzzy calculus concepts such as differentiation and integration for the derivation, manipulation and solution of the finite element equations. Simple stress analysis problems involving vaguely defined geometry, material properties, external loads and boundary conditions are solved to establish and to illustrate the new procedure. The approach developed is applicable to systems that are described in linguistic terms as well as those that are described by incomplete information. If complete data are known, the method handles the information similar to that of a probabilistic approach. The present approach represents a unique methodology that enables us to handle certain types of imprecisely known data more realistically compared with the existing procedures.

UR - http://www.scopus.com/inward/record.url?scp=0029710707&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029710707&partnerID=8YFLogxK

M3 - Conference contribution

VL - 4

SP - 2519

EP - 2529

BT - Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

PB - AIAA

ER -