On the displacement boundary-value problem of static linear elasticity theory

1968 ◽  
Vol 19 (2) ◽  
pp. 219-233 ◽  
Author(s):  
Roger L. Fosdick
Keyword(s):  
Boundary Value Problem ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Boundary Value ◽  
Linear Elasticity Theory ◽  
Displacement Boundary

scholarly journals Boundary value problems for the Lamé-Navier system in fractal domains

2021 ◽  
Vol 6 (10) ◽  
pp. 10449-10465
Author(s):  
Ricardo Abreu Blaya ◽  
◽  
J. A. Mendez-Bermudez ◽  
Arsenio Moreno García ◽  
José M. Sigarreta ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Representation Formula ◽  
Linear Elasticity Theory ◽  
Fractal Domains

<abstract><p>The aim of this paper is to establish a representation formula for the solutions of the Lamé-Navier system in linear elasticity theory. We also study boundary value problems for such a system in a bounded domain $ \Omega\subset {\mathbb R}^3 $, allowing a very general geometric behavior of its boundary. Our method exploits the connections between this system and some classes of second order partial differential equations arising in Clifford analysis.</p></abstract>

scholarly journals Linear elasticity theory free from diffeomorphism: plane deformation

2020 ◽  
pp. 162-167
Author(s):  
Ольга Александровна Микенина ◽  
Александр Филиппович Ревуженко
Keyword(s):  
Boundary Value Problem ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Classical Model ◽  
Plane Deformation ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Linear Elasticity Theory ◽  
Unicity Theorem ◽  
Two Dimensional Model

Строится плоская модель линейно упругого тела, в которой постулат о диффеоморфизме (предположение о гладкости поля перемещений) значительно ослаблен. Вместо одного поля перемещений, которое фигурирует в классической модели, вводятся два гладких поля перемещений. Рассмотрены постановки краевых задач, доказана теорема единственности. The authors create a two-dimensional model of a linearly elastic body at considerably weakened postulate of diffeomorphism-supposed smoothness of field of displacements. One field of displacements as in the classical model is replaced by two smooth fields of displacements. The authors discuss formulations of boundary value problem and prove the unicity theorem

Linear elasticity theory of cubic quasicrystals

1993 ◽  
Vol 48 (10) ◽  
pp. 6999-7002 ◽  
Author(s):  
Wenge Yang ◽  
Renhui Wang ◽  
Di-hua Ding ◽  
Chengzheng Hu
Keyword(s):  
Elasticity Theory ◽  
Linear Elasticity ◽  
Linear Elasticity Theory

Elastodynamics. Sinusoidal progressive waves

2020 ◽  
pp. 251-254
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Boundary Value Problem ◽  
Linear Elasticity ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Important Class ◽  
Linear Elastodynamics ◽  
Isotropic Media ◽  
Progressive Waves ◽  
Initial Boundary Value

This chapter briefly considers linear elasticity under circumstances in which inertial effects are accounted for, and states the initial-boundary-value-problem of linear elastodynamics. Sinusoidal progressive waves form an important class of solutions to the equations of linear elastodynamics. Such waves for isotropic media in the absence of a conventional body force are considered and it is shown that for an isotropic medium only two types of sinusoidal progressive waves are possible: longitudinal and transverse.

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