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Start Over Creator Franců, Jan

2. Homogenization of diffusion equation with scalar hysteresis operator

Creator:
Franců, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
hysteresis, Prandtl-Ishlinskii operator, material with periodic structure, nonlinear diffusion equation, and homogenization
Language:
English
Description:
The paper deals with a scalar diffusion equation c ut = (F[ux])x+f, where F is a Prandtl-Ishlinskii operator and c, f are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic data cε and ηε when the spatial period ε tends to zero. The homogenized characteristics c∗ and η∗ are identified and the convergence of the corresponding solutions to the solution of the homogenized equation is proved.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Modification of unfolding approach to two-scale convergence

Creator:
Franců, Jan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
homogenization, two-scale convergence, and periodic unfolding
Language:
English
Description:
Two-scale convergence is a powerful mathematical tool in periodic homogenization developed for modelling media with periodic structure. The contribution deals with the classical definition, its problems, the ''dua''' definition based on the so-called periodic unfolding. Since in the case of domains with boundary the unfolding operator introduced by D. Cioranescu, A. Damlamian, G. Griso does not satisfy the crucial integral preserving property, the contribution proposes a modified unfolding operator which satisfies the property and thus simplifies the theory. The properties of two-scale convergence are surveyed.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Torsion of a bar with holes

Creator:
Franců, Jan and Rozehnalová-Nováčková, Petra
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
torsion of non-circular bar, Airy stress function, and profile with holes
Language:
English
Description:
The contribution is a continuation of [2] which deals with analytic solution of torsion of a bar with simply connected profile, i.e. profile without holes. In this paper the case of multiply connected profile, i.e. profile with holes, is studied. The stress-strain analysis leads to the Airy stress function Φ. On boundary of each hole the function Φ has prescribed an unknown constant value completed with an integral condition. The mathematical model is also derived from the variational principle. The second part of the paper contains solutions for the ring profile and for comparison also for incomplete ring profiles including the ‘broken‘ ring profile. The results are compared in tables and pictures. and Obsahuje seznam literatury
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public

5. Torsion of a non-circular bar

Creator:
Franců, Jan, Nováčková, Petra, and Janíček, Přemysl
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
torsion of non-circular bar, Airy stress function, and rectangular profile
Language:
English
Description:
The contribution deals with strain-stress analysis of torsion of a non-circular bar. Mathematical model is exactly derived and solutions are introduced and visualised for cases of triangular, rectangular and some other profiles. and Obsahuje seznam literatury
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public