Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 9

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Regularity of displacement solutions in Hencky plasticity. I: The extremal relation

100%
Bojarski J.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 3
259-293
EN
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. A non-homogeneous material whose elastic-plastic properties change discontinuously is considered. We find (in an explicit form) the extremal relation between the displacement formulation (defined on the space of bounded deformation) and the stress formulation of the variational problem in Hencky plasticity. This extremal relation is used in the proof of the regularity of displacements. In part II of the paper, we will prove that the displacement solution belongs to the classical Sobolev space (if the stress solution belongs to the interior of a set of admissible stresses, at each point). We will find the regularity theorem for displacement solutions in composite materials whose elastic-plastic properties may change discontinuously.
2
Content available remote

Regularity of displacement solutions in Hencky plasticity. II: The main result

100%
Bojarski J.
Applicationes Mathematicae
|
2011
|
tom 38
|
nr 4
413-434
EN
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity. In the second part, we prove that the displacement solution belongs to the appropriate Sobolev space (if the stress solution belongs to the interior of a set of admissible stresses, at each point). Then we deduce a regularity theorem for displacement solutions in composite materials.
3
Content available remote

Regularity of solutions in plasticity. II: Plates

100%
Bojarski J.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 1
31-54
EN
The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. We consider a plate made of a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space $W^{2,1}(Ω)$ if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.
4
Content available remote

Regularization of noncoercive constraints in Hencky plasticity

100%
Bojarski J.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 3
327-340
EN
The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.
5
Content available remote

General method of regularization. II: Relaxation proposed by suquet

100%
Bojarski J.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 3
321-343
EN
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. We show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we prove an existence theorem for the limit analysis problem.
6
Content available remote

The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity

100%
Bojarski J.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 4
443-464
EN
The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.
7
Content available remote

General method of regularization. III: The unilateral contact problem

100%
Bojarski J.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 4
473-492
EN
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. We deduce that the relaxation of the energy of plastic soil (with the Signorini condition on the boundary) is the weak* lower semicontinuous regularization of the energy.
8
Content available remote

Regularity of solutions in plasticity. I: Continuum

100%
Bojarski J.
Applicationes Mathematicae
|
2003
|
tom 30
|
nr 3
337-364
EN
The aim of this paper is to study the problem of regularity of solutions in Hencky plasticity. We consider a non-homogeneous material whose elastic-plastic properties change discontinuously. We prove that the displacement solutions belong to the space $LD(Ω) ≡ {u ∈ L¹(Ω,ℝⁿ) | ∇u + (∇u)^{T} ∈ L¹(Ω,ℝ^{n×n})}$ if the stress solution is continuous and belongs to the interior of the set of admissible stresses, at each point. The part of the functional which describes the work of boundary forces is relaxed.
9
Content available remote

General method of regularization. I: Functionals defined on BD space

100%
Bojarski J.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 2
175-199
EN
The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis problem.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.