Fuzzy meshless local Petrov-Galerkin method for analysis of imprecisely defined systems

Singiresu S Rao, Jun Tian

Research output: Contribution to journalArticle

Abstract

Many engineering systems contain uncertainties that cannot be described by either deterministic or probabilistic approaches. For example, the geometry, material properties, external actions (loads), and boundary conditions may be imprecise in a practical mechanical or structural system. The uncertainties present may be associated with parameters that are vague, imprecise, or linguistic. A fuzzy meshless local Petrov-Galerkin approach is developed in this work for the analysis of imprecisely defined systems. Starting from the basic concepts of fuzzy sets, fuzzy arithmetic, and fuzzy calculus (differentiation and integration) the various steps of the meshless local Petrov-Galerkin approach involved in the derivation of the equations are redefined using fuzzy concepts. The resulting fuzzy equations are derived using a fuzzy version of Gaussian elimination procedure coupled with truncation. A one-dimensional heat-transfer problem involving conduction, convection, and radiation with vaguely defined thermal properties of the material and boundary conditions and two stress-analysis problems (a beam and a plate with a hole) with vaguely defined material properties and external loads are considered to demonstrate the methodology. A truncation scheme is used to overcome the difficulty of overestimating the width of the response characteristics of the system due to repeated fuzzy arithmetic operations in the solution of the fuzzy equations.Asimple sequential linearization scheme is used to handle the nonlinear boundary-value problem associated with the radiation boundary condition in the heat-transfer problem. The present approach represents a unique methodology that enables the handling of certain types of imprecisely known data more realistically compared to the existing procedures.

Original languageEnglish
Pages (from-to)1320-1332
Number of pages13
JournalAIAA Journal
Volume51
Issue number6
DOIs
StatePublished - Jun 1 2013

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Galerkin methods
Computer systems
Boundary conditions
Materials properties
Heat transfer
Radiation
Fuzzy sets
Stress analysis
Systems engineering
Linearization
Linguistics
Boundary value problems
Thermodynamic properties
Geometry
Uncertainty

ASJC Scopus subject areas

  • Aerospace Engineering

Cite this

Fuzzy meshless local Petrov-Galerkin method for analysis of imprecisely defined systems. / Rao, Singiresu S; Tian, Jun.

In: AIAA Journal, Vol. 51, No. 6, 01.06.2013, p. 1320-1332.

Research output: Contribution to journalArticle

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