Boundary-value problem of dynamic geometrically nonlinear elasticity

1994 ◽  
Vol 35 (6) ◽  
pp. 942-948
Author(s):  
V. D. Bondar'
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Elasticity ◽  
Boundary Value ◽  
Geometrically Nonlinear

scholarly journals Stability of a composite thick plate with an inhomogeneous field of initial stresses

2018 ◽  
Vol 226 ◽  
pp. 01013
Author(s):  
Vadim V. Eremeev ◽  
Natalia Y. Shubchinskaya ◽  
Denis V. Ivashchenko ◽  
Vsevolod A. Minko
Keyword(s):  
Stability Analysis ◽  
Boundary Value Problem ◽  
Linear Stability ◽  
Nonlinear Elasticity ◽  
Elastic Plate ◽  
Linear Stability Analysis ◽  
Thick Plate ◽  
Boundary Value ◽  
Initial Stresses ◽  
Inhomogeneous Field

We discuss the linear stability analysis for a rectangular twolayered elastic plate. Each layer of the plate was obtained due to inflation of an annular wedge of a cylinder. As a result, in the plate there are initial stresses. The main aim of the paper is to analyse the influence of the initial stresses on the buckling. Here we use the 3D nonlinear elasticity technique. The linearized boundary-value problem is derived and its non-trivial solutions were obtained.

STABILITY OF EQUILIBRIUM STATES OF NONLINEAR STRUCTURES AND CHAOS PHENOMENON.

1992 ◽  
Vol 02 (02) ◽  
pp. 271-283 ◽  
Author(s):  
D. SHILKRUT
Keyword(s):  
Boundary Value Problem ◽  
Finite Interval ◽  
Boundary Value ◽  
Geometrically Nonlinear ◽  
Geometrical Approach ◽  
Initial Value ◽  
Nonlinear Structure ◽  
Deterministic Systems ◽  
Classical Chaos ◽  
Problem Characteristic

The “classical” chaos of deterministic systems is characteristic for the motion of dynamical systems. Recently, some attempts were made to find static analogies of chaos [Thompson & Virgin, 1988; Naschie & Athel, 1989; Naschie, 1989]. However, this was considered for structures in specific artificial conditions (for example, infinitely long bars with sinusoidal geometric imperfections) transferring de facto the boundary value problem (which always describes static deformation of structures) into an initial value problem characteristic for problems of motion. In this article, chaotic (unpredictable) behavior is described for a usual (not special) nonlinear structure in statics, which is governed, naturally, by a boundary value problem in a finite interval of the argument. The behavior of this structure (geometrically nonlinear plate), which is an example of the class of static chaotic structures, is investigated by a new geometrical approach called the “deformation map.” The presented results are one of the first steps in the chapter of chaos in statics, and therefore the link between “classical” and static chaos needs further investigations.

AXIAL-SYMMETRIC BOUNDARY VALUE PROBLEM WITH NONLINEAR ELASTICITY

AIAA Journal ◽  
1963 ◽  
Vol 1 (4) ◽  
pp. 948-948
Author(s):  
M. BIENIEK ◽  
W. R. SPILLERS
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Elasticity ◽  
Boundary Value

A construction of infinitely many singular weak solutions to the equations of nonlinear elasticity

2002 ◽  
Vol 132 (4) ◽  
pp. 985-992 ◽  
Author(s):  
J. Sivaloganathan ◽  
S. J. Spector
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Elasticity ◽  
Elastic Material ◽  
Weak Solutions ◽  
Boundary Value ◽  
Nonlinear Elastic Material ◽  
Displacement Boundary ◽  
Nonlinear Elastic

Radial deformations of a ball composed of a nonlinear elastic material and corresponding to cavitation have been much studied. In this paper we use rescalings to show that each such deformation can be used to construct infinitely many non-symmetric singular weak solutions of the equations of nonlinear elasticity for the same displacement boundary-value problem. Surprisingly, this property appears to have been unnoticed in the literature to date.

On the asymptotic behaviour at infinity of solutions of the traction boundary value problem

1989 ◽  
Vol 111 (1-2) ◽  
pp. 33-52 ◽  
Author(s):  
B.B. Orazov
Keyword(s):  
Boundary Value Problem ◽  
Asymptotic Behaviour ◽  
Nonlinear Elasticity ◽  
Boundary Value ◽  
Asymptotic Behaviour Of Solutions

SynopsisKorn's inequalities are proved for star-shaped domains and it is shown how the constants in these inequalities depend on the dimensions of the domain. These inequalities are then used to prove a generalisation of Saint-Venant's Principle for nonlinear elasticity and additionally to establish the asymptotic behaviour of solutions to the traction boundary value problem for a non-prismatic cylinder.

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