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Partial Fourier approximation of the Lamé equations in axisymmetric domains

In this paper, we study the partial Fourier method for
treating the Lamé equations in three-­dimensional
axisymmetric domains subjected to nonaxisymmetric loads.
We consider the mixed boundary value problem of the
linear theory of elasticity with the displacement u,
the body force f \in (L_2)^3 and homogeneous Dirichlet
and Neumann boundary conditions. The partial Fourier
decomposition reduces, without any error, the
three­dimensional boundary value problem to an infinite
sequence of two­dimensional boundary value problems,
whose solutions u_n (n = 0,1,2,...) are the Fourier
coefficients of u. This process of dimension reduction
is described, and appropriate function spaces are given
to characterize the reduced problems in two dimensions.
The trace properties of these spaces on the rotational
axis and some properties of the Fourier coefficients u_n
are proved, which are important for further numerical
treatment, e.g. by the finite-element method.
Moreover, generalized completeness relations are described
for the variational equation, the stresses and the strains.
The properties of the resulting system of two­dimensional
problems are characterized. Particularly, a priori
estimates of the Fourier coefficients u_n and of the error
of the partial Fourier approximation are given.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:18362
Date14 September 2005
CreatorsNkemzi, Boniface, Heinrich, Bernd
PublisherTechnische Universität Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint, info:eu-repo/semantics/preprint, doc-type:Text
SourcePreprintreihe des Chemnitzer SFB 393, 98-26
Rightsinfo:eu-repo/semantics/openAccess

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