On fractional non-local bodies with variable length scale |
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| Affiliation: | 1. CEA, DEN, DANS, DM2S, SEMT, Laboratoire d’Études de Mécanique Sismique, F-91191 Gif-sur-Yvette, France;2. LMT, ENS Cachan, CNRS, Université Paris-Saclay, 61 avenue du Président Wilson, F-94230 Cachan, France;1. Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States;2. Department of Civil Engineering and Computer Science, University of Rome “Tor Vergata”, Via del Politecnico 1, 00133 Rome, Italy;3. Université Pierre et Marie Curie, Institut D’Alembert, UMR 7190 CNRS, 4 Place Jussieu, 75252 Paris Cedex 05, France |
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| Abstract: | This paper discusses the application of the variable length scale concept in the framework of non-local fractional model. The considerations are motivated by the fact that real material characteristic dimension is never uniform and simultaneously the problem of existence of the virtual boundary layer in the boundary value problems, discussed in previous papers, is removed. The considerations are illustrated with a series of analyses of 1D elasticity problems. Nonetheless, the conclusions are applicable for an arbitrary configurations. |
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| Keywords: | Non-local models Fractional calculus Variable length scale |
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