On general boundary value problems and duality in linear elasticity. I

Rolf Hünlich; Joachim Naumann

Aplikace matematiky (1978)

  • Volume: 23, Issue: 3, page 208-230
  • ISSN: 0862-7940

Abstract

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The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as special cases all known classical, bilateral and unilateral boundary conditions. Further, the principle of virtual displacements and the principle of minimum of the potential energy are established and it is shown that these principles are equivalent to the original boundary condition problem.

How to cite

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Hünlich, Rolf, and Naumann, Joachim. "On general boundary value problems and duality in linear elasticity. I." Aplikace matematiky 23.3 (1978): 208-230. <http://eudml.org/doc/15051>.

@article{Hünlich1978,
abstract = {The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as special cases all known classical, bilateral and unilateral boundary conditions. Further, the principle of virtual displacements and the principle of minimum of the potential energy are established and it is shown that these principles are equivalent to the original boundary condition problem.},
author = {Hünlich, Rolf, Naumann, Joachim},
journal = {Aplikace matematiky},
keywords = {boundary value problems; linear elasticity; law of interaction; principle of virtual displacements; principal of minimum potential energy; Boundary Value Problems; Linear Elasticity; Law of Interaction; Principle of Virtual Displacements; Principal of Minimum Potential Energy},
language = {eng},
number = {3},
pages = {208-230},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On general boundary value problems and duality in linear elasticity. I},
url = {http://eudml.org/doc/15051},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Hünlich, Rolf
AU - Naumann, Joachim
TI - On general boundary value problems and duality in linear elasticity. I
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 3
SP - 208
EP - 230
AB - The equilibrium state of a deformable body under the action of body forces is described by the well known conditions of equilibrium, the straindisplacement relations, the constitutive law of the linear theory and the boundary conditions. The authors discuss in detail the boundary conditions. The starting point is the general relation between the vectors of stress and displacement on the boundary which can be expressed in terms of a subgradient relation. It is shown that this relation includes as special cases all known classical, bilateral and unilateral boundary conditions. Further, the principle of virtual displacements and the principle of minimum of the potential energy are established and it is shown that these principles are equivalent to the original boundary condition problem.
LA - eng
KW - boundary value problems; linear elasticity; law of interaction; principle of virtual displacements; principal of minimum potential energy; Boundary Value Problems; Linear Elasticity; Law of Interaction; Principle of Virtual Displacements; Principal of Minimum Potential Energy
UR - http://eudml.org/doc/15051
ER -

References

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  14. B. Nayroles, Quelques applications variationnelles de la théorie des functions duales à la mécanique de solides, J. Méc., 10 (1971), 263-289. (1971) MR0280053
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