Interval Finite Element Method

Finite element method (FEM) combined with interval uncertainties are referred to as interval FEM which has already been used in various structural systems. On the other hand, for fuzzy uncertainties FEM is known as fuzzy FEM discussed for uncertain structural systems. In structural mechanics, the FE...

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Vydáno v:Advanced Numerical and Semi-Analytical Methods for Differential Equations s. 217 - 229
Hlavní autoři: Chakraverty, Snehashish, Mahato, Nisha, Karunakar, Perumandla, Dilleswar Rao, Tharasi
Médium: Kapitola
Jazyk:angličtina
Vydáno: United States Wiley 2019
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Vydání:1
Témata:
dynamic analysis
eigenvalue problems
Galerkin FEM
interval boundary conditions
interval finite element method
interval uncertainties
one‐dimensional structural system
ordinary differential equation
static analysis
Fuzzy sets
Uncertainty
Boundary conditions
Eigenvalues and eigenfunctions
Finite element analysis
Mathematical model
Method of moments
ISBN:9781119423423, 1119423422
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Shrnutí:Finite element method (FEM) combined with interval uncertainties are referred to as interval FEM which has already been used in various structural systems. On the other hand, for fuzzy uncertainties FEM is known as fuzzy FEM discussed for uncertain structural systems. In structural mechanics, the FEM converts the governing differential equation of static and dynamic problems of structural systems having interval uncertainties to interval system of equations and interval eigenvalue problem, respectively. In this regard, the chapter presents the introduction and preliminaries related to system of equations and eigenvalue problems with uncertain (in terms of interval) parameters. It provides a detailed procedure for solving ordinary differential equation subject to interval boundary conditions using Galerkin FEM. As such, the authors refer the Galerkin FEM for solving differential equation with interval uncertainties as uncertain IGFEM. Lastly, the chapter considers uncertain static and dynamic analysis of one‐dimensional structural system.
ISBN:9781119423423
1119423422
DOI:10.1002/9781119423461.ch21