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Computational and Applied Mathematics : Volume 36

Computational and Applied Mathematics : Volume 35

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Global GPBiCG method for complex non-Hermitian linear systems with multiple right-hand sides

Solution of the direct and inverse problems for beam

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Efficient derivative-free numerical methods for solving systems of nonlinear equations

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Computational and Applied Mathematics : Volume 34

Computational and Applied Mathematics : Volume 33

Computational and Applied Mathematics : Volume 32

Solution of the direct and inverse problems for beam

Content Provider	Springer Nature Link
Author	Pawinska, Anna Maciag, Artur
Copyright Year	2014
Abstract	The article presents an approximate method of solving direct and inverse problems described by Bernoulli–Euler inhomogeneous equation of vibrations of a beam. A semianalytical solution is approximated by a linear combination of the Trefftz functions (T-functions, solving functions), which satisfies identically the homogenous equation describing the vibrations of a beam. In the paper, the properties of the solving functions have been investigated, theorems concerning their linear independence have been formulated and proved. A method of obtaining the particular solution of the inhomogeneous equation has been shown. To get this solution, recurrent formulas enabling us to determine the inverse operator for monomials have been derived. The paper discusses two kinds of inverse problems. The first one is a boundary inverse problem, in which the boundary conditions are to be determined, based on known displacements within the area. In the second one, the load on the beam needs to be found (identification of the source). The solving functions can be used as a finite element method base functions. This approach is tested for solving inverse problems. The paper includes examples which illustrate the usefulness of the method.
Starting Page	187
Ending Page	201
Page Count	15
File Format	PDF
ISSN	01018205
Journal	Computational and Applied Mathematics
Volume Number	35
Issue Number	1
e-ISSN	18070302
Language	English
Publisher	Springer International Publishing
Publisher Date	2014-10-11
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computational Mathematics and Numerical Analysis Trefftz function Nodeless FEM Rods Boundary inverse problems Linear higher-order equations Source identification Inverse problems Particular solution Mathematical Applications in Computer Science Linear independence Applications of Mathematics Mathematical Applications in the Physical Sciences Beam vibration
Content Type	Text
Resource Type	Article

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