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The stiffness of self-similar fractals
- Source :
-
International Journal of Solids & Structures . Jun2008, Vol. 45 Issue 11/12, p3238-3254. 17p. - Publication Year :
- 2008
-
Abstract
- Abstract: A method to derive the stiffness of self-similar elastic fractals is presented based on structural mechanics principles and a physically motivated similarity criterion, which is assumed as a postulate. Using this method, the stiffnesses of both the Von Koch curve and the Sierpiński gasket in the small-deformation regime are derived. For these fractal structures, it is shown that the stiffness matrix is completely determined by a single elastic constant. The procedure to tile a planar domain with Sierpiński gaskets is explored and shown to require the consideration of hexagonal-shaped combinations of gaskets joined continuously along their edges. This continuity leads to a phenomenon of geometrically induced inextensibility along the common edges. After deriving the stiffness matrix for the basic hexagon, the analog of the Boussinesq–Flamant problem for a tiled half-plane is solved numerically to demonstrate the potential of the method in modeling of solid mechanics applications. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 00207683
- Volume :
- 45
- Issue :
- 11/12
- Database :
- Academic Search Index
- Journal :
- International Journal of Solids & Structures
- Publication Type :
- Academic Journal
- Accession number :
- 31679718
- Full Text :
- https://doi.org/10.1016/j.ijsolstr.2008.01.022