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On static analysis of finite repetitive structures by discrete Fourier transform

On static analysis of finite repetitive structures by discrete Fourier transform
On static analysis of finite repetitive structures by discrete Fourier transform
Functional solutions for the static response of beam- and plate-like repetitive lattice structures are obtained by discrete Fourier transform. The governing equation is set up as a single operator form with the physical stiffness operator acting as a convolution sum and containing a matrix kernel, which relates to the mechanical properties of the lattice. Boundary conditions do not affect the equation form, and are taken into account at a subsequent stage of the analysis. The technique of virtual load and substructure is proposed to formally close the repetitive lattice into a cyclic structure, and to assure the equivalence of responses of the modified cyclic and original repetitive lattices. A discrete periodic Green's function is introduced for the modified structure, and the final displacement solutions are written as convolution sums over the Green's function and the actual external and virtual loads. Several example problems illustrate the approach.
repetitive structures, static response, discrete fourier transform, green's function
0020-7683
4291-4310
Karpov, E.G.
5479efe4-a7fa-49c0-9730-c1e6f0cc0d4f
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Dorofeev, D.L.
049aefe5-d084-439b-b4c7-86c18b869005
Karpov, E.G.
5479efe4-a7fa-49c0-9730-c1e6f0cc0d4f
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Dorofeev, D.L.
049aefe5-d084-439b-b4c7-86c18b869005

Karpov, E.G., Stephen, N.G. and Dorofeev, D.L. (2002) On static analysis of finite repetitive structures by discrete Fourier transform. International Journal of Solids and Structures, 39 (16), 4291-4310. (doi:10.1016/S0020-7683(02)00259-7).

Record type: Article

Abstract

Functional solutions for the static response of beam- and plate-like repetitive lattice structures are obtained by discrete Fourier transform. The governing equation is set up as a single operator form with the physical stiffness operator acting as a convolution sum and containing a matrix kernel, which relates to the mechanical properties of the lattice. Boundary conditions do not affect the equation form, and are taken into account at a subsequent stage of the analysis. The technique of virtual load and substructure is proposed to formally close the repetitive lattice into a cyclic structure, and to assure the equivalence of responses of the modified cyclic and original repetitive lattices. A discrete periodic Green's function is introduced for the modified structure, and the final displacement solutions are written as convolution sums over the Green's function and the actual external and virtual loads. Several example problems illustrate the approach.

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More information

Published date: 2002
Keywords: repetitive structures, static response, discrete fourier transform, green's function

Identifiers

Local EPrints ID: 22063
URI: http://eprints.soton.ac.uk/id/eprint/22063
ISSN: 0020-7683
PURE UUID: 9d329911-5735-41d6-b46c-0d66ffb464ac

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Date deposited: 14 Mar 2006
Last modified: 15 Mar 2024 06:34

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Contributors

Author: E.G. Karpov
Author: N.G. Stephen
Author: D.L. Dorofeev

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