2014/10/18 by Vasily E. Tarasov
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Composite Material Mechanics #Computer science #Elasticity (physics) #Finite element method #Fractal #Fractal analysis #Fractal derivative #Fractal dimension #Fractal dimension on networks #Integer (computer science) #Linear elasticity #Mathematical analysis #Mathematics #Nonlocal and gradient elasticity in micro/nano structures #Physics #Thermodynamics #Thermoelastic and Magnetoelastic Phenomena #cond-mat.mtrl-sci #physics.geo-ph
paper · pdf · doi:10.1016/j.crme.2014.09.006
published as Comptes Rendus Mecanique. Vol.343. No.1. (2015) 57-73 · 28 pages, LaTeX. arXiv admin note: substantial text overlap with arXiv:1503.02022, arXiv:1503.02842
openalex publication_date 2014/10/18 · arxiv created 2015/03/10 · arxiv updated 2015/03/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.