Asymptotic representation of elastic fields in a multi-structure

Article type: Research Article

Authors: Kozlov, V.A.^; | Maz'ya, V.G. | Movchan, A.B.^;

Affiliations: Department of Mathematics, University of Linköping, S-581 83 Linköping, Sweden | School of Mathematical Sciences, University of Bath Bath, Ba2 7AY, U.K.

Note: [] V.A. Kozlov was supported by the Royal Swedish Academy of Science and the Swedish Council for Engineering Sciences (TFR) under the “Linköping International Centre for Applied and Industrial Mathematics”. During his work at the University of Bath V.A. Kozlov was supported by the research fellowship grant GR/J89354 from the UK Science and Engineering Research Council.

Note: [] A.B. Movchan is grateful for the financial support of Linköping University during his visits to Sweden.

Abstract: A mixed boundary value problem is posed for the Lame system in an elastic multi-structure which consists of a union of a three-dimensional domain and thin cylinders. A normalized thickness of a rod is characterized by a small parameter ε. We present a rigorous algorithm which yields a multi-scaled asymptotic expansion for the displacement and stress fields in the multi-structure. Justification of the asymptotic algorithm, including the remainder estimate for the asymptotic approximation of the displacement field, is given. The asymptotic analysis provides the range of applicability of the engineering pile structure model. It is shown that first three eigenvalues of the spectral problem in the above multi-structure have the order O(ε4). The asymptotic formulae for these eigenvalues are obtained.

DOI: 10.3233/ASY-1995-11402

Journal: Asymptotic Analysis, vol. 11, no. 4, pp. 343-415, 1995