Unilateral contact problems with fractal geometry and fractal friction laws: methods of calculation |
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Authors: | E S Mistakidis O K Panagouli P D Panagiotopoulos |
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Affiliation: | (1) Institute of Steel Structures, Aristotle University, GR-54006 Thessaloniki, Greece, GR |
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Abstract: | The present paper deals with two interrelated subjects: the fractal geometry and the fractal behaviour in unilateral contact
problems. More specifically, throughout this paper both the interfaces and the friction laws holding on these interfaces are
modelled by means of the fractal geometry. It is important to notice here that the fractality of the induced friction laws
takes into account the randomness of the interface asperities causing the friction forces. According to the fractal model
introduced in this paper, both the fractal law and the fractal interface are considered to be graphs of two different fractal
interpolation functions which are the “fixed points” of two contractive operators. Using this method, the fractal friction
law is approximated by a sequence of nonmonotone possibly multivalued classical C
0-curves. The numerical treatment of each arizing nonmonotone problem is accomplished by an advanced solution method which
approximates the nonmonotone problem by a sequence of monotone subproblems. Numerical applications from the static analysis
of cracked structures with a prescribed fractal geometry and fractal interface laws are included in order to illustrate the
theory. |
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Keywords: | |
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