Unilateral contact problems with fractal geometry and fractal friction laws: Methods of calculation
type: Item
instance of: scholarly article
title: Unilateral contact problems with fractal geometry and fractal friction laws: Methods of calculation
zbMATH Open document ID: 0915.73052
author: E. S. Mistakidis
author: O. K. Panagouli
author: Panagiotis D. Panagiotopoulos
published in: Computational Mechanics
publication date: 1999-07-07T00:00:00Z
review text: We deal with two interrelated subjects: the fractal geometry and the fractal behaviour in unilateral contact problems. More specifically, both the interfaces and the friction laws holding on these interfaces are modelled by means of the fractal geometry. According to the fractal model, the fractal law and the fractal interface are considered to be graphs of two different fractal interpolation functions which are ``fixed points'' of two contractive operators. Using this method, we approximate the fractal friction law by a sequence of nonmonotone possibly multivalued classical \(C^0\)-curves. The numerical treatment of the arising nonmonotone problem is accomplished by an advanced solution method which approximates the nonmonotone problem by a sequence of monotone subproblems. Numerical applications to cracked structures with a prescribed fractal geometry and fractal interface laws illustrate the theory.
Mathematics Subject Classification ID: 74A55
Mathematics Subject Classification ID: 74M15
Mathematics Subject Classification ID: 28A80
zbMATH DE Number: 1221206
zbMATH Keywords: fixed points
zbMATH Keywords: fractal interpolation functions
zbMATH Keywords: contractive operators
zbMATH Keywords: nonmonotone problem
zbMATH Keywords: sequence of monotone subproblems
zbMATH Keywords: cracked structures
MaRDI profile type: Publication
full work available at URL: s004660050312
OpenAlex ID: W2022284351
DOI: 10.1007/S004660050312
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description: scientific article; zbMATH DE number 1221206