𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Partial Fourier approximation of the Lamé equations in axisymmetric domains

✍ Scribed by Boniface Nkemzi; Bernd Heinrich

Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
212 KB
Volume
22
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

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

📜 SIMILAR VOLUMES

On solution of Lamé equations in axisymm
On solution of Lamé equations in axisymmetric domains with conical points
✍ Boniface Nkemzi 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB

## Abstract Partial Fourier series expansion is applied to the Dirichlet problem for the Lamé equations in axisymmetric domains $\hat{\Omega}$⊂ℝ^3^ with conical points on the rotation axis. This leads to dimension reduction of the three‐dimensional boundary value problem resulting to an infinite se

On the absence of eigenvalues of Maxwell
On the absence of eigenvalues of Maxwell and Lamé systems in exterior domains
✍ Sebastian Bauer 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 132 KB

## Abstract The arguments showing non‐existence of eigensolutions to exterior‐boundary value problems associated with systems—such as the Maxwell and Lamé system—rely on showing that such solutions would have to have compact support and therefore—by a unique continuation property—cannot be non‐triv