Applied Mathematics and Mechanics

, Volume 23, Issue 9, pp 1054–1061

# Fuzzy arithmetic and solving of the static governing equations of fuzzy finite element method

• Guo Shu-xiang
• Lü Zhen-zhou
• Feng Li-fu
Article

## Abstract

The key component of finite element analysis of structures with fuzzy parameters, which is associated with handling of some fuzzy information and arithmetic relation of fuzzy variables, was the solving of the governing equations of fuzzy finite element method. Based on a given interval representation of fuzzy numbers, some arithmetic rules of fuzzy numbers and fuzzy variables were developed in terms of the properties of interval arithmetic. According to the rules and by the theory of interval finite element method, procedures for solving the static governing equations of fuzzy finite element method of structures were presented. By the proposed procedure, the possibility distributions of responses of fuzzy structures can be generated in terms of the membership functions of the input fuzzy numbers. It is shown by a numerical example that the computational burden of the presented procedures is low and easy to implement. The effectiveness and usefulness of the presented procedures are also illustrated.

## Key words

fuzzy variable fuzzy arithmetic fuzzy finite element method interval finite element method

TB115 O159

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© Editorial Committee of Applied Mathematics and Mechanics 1980

## Authors and Affiliations

• Guo Shu-xiang
• 1
• Lü Zhen-zhou
• 2
• Feng Li-fu
• 1
1. 1.Faculty of Mechanics, Engineering InstituteAir Force University of EngineeringXi’anP R China
2. 2.Department of Aircraft EngineeringNorthwest Polytechnical UniversityXi’anP R China