Studies of quality of geometrically nonlinear elasticity theory for small strains and arbitrary displacements

2009 ◽  
Vol 44 (6) ◽  
pp. 837-851 ◽  
Author(s):  
D. V. Berezhnoi ◽  
V. N. Paimushin ◽  
V. I. Shalashilin
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Elasticity ◽  
Geometrically Nonlinear ◽  
Nonlinear Elasticity Theory ◽  
Small Strains

scholarly journals MATHEMATICAL MODELING IN GEOMETRICALLY NONLINEAR ELASTICITY THEORY PROBLEMS

2021 ◽  
Vol 4 (1) ◽  
pp. 103-110
Author(s):  
T.S. KAGADIY ◽  
A.H. SHPORTA ◽  
I.V. SCHERBINA ◽  
О.V. BILOVA
Keyword(s):  
Mathematical Modeling ◽  
Elasticity Theory ◽  
Nonlinear Elasticity ◽  
Geometrically Nonlinear ◽  
Nonlinear Elasticity Theory

Multivalued displacements and volterra dislocations in plane nonlinear elasticity theory

1988 ◽  
Vol 28 (6) ◽  
pp. 934-939 ◽  
Author(s):  
L. M. Zubov ◽  
M. I. Karyakin
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Elasticity ◽  
Nonlinear Elasticity Theory

Influence of Distributed Dislocations on Stability of Hollow Nonlinearly Elastic Sphere

2020 ◽  
pp. 17-21
Author(s):  
Evgeniya V. Goloveshkina
Keyword(s):  
Boundary Value Problem ◽  
Elasticity Theory ◽  
Elastic Body ◽  
Nonlinear Elasticity ◽  
External Pressure ◽  
Elastic Sphere ◽  
Unperturbed State ◽  
Nonlinear Elasticity Theory ◽  
Edge Dislocations ◽  
Distributed Dislocations

The phenomenon of stability loss of a hollow elastic sphere containing distributed dislocations and loaded with external hydrostatic pressure is studied. The study was carried out in the framework of the nonlinear elasticity theory and the continuum theory of continuously distributed dislocations. An exact statement and solution of the stability problem for a three-dimensional elastic body with distributed dislocations are given. The static problem of nonlinear elasticity theory for a body with distributed dislocations is reduced to a system of equations consisting of equilibrium equations, incompatibility equations with a given dislocation density tensor, and constitutive equations of the material. The unperturbed state is caused by external pressure and a spherically symmet-ric distribution of dislocations. For distributed edge dislocations in the framework of a harmonic (semi-linear) mate-rial model, the unperturbed state is defined as an exact spherically symmetric solution to a nonlinear boundary value problem. This solution is valid for any function that characterizes the density of edge dislocations. The perturbed equilibrium state is described by a boundary value problem linearized in the neighborhood of the equilibrium. The analysis of the axisymmetric buckling of the sphere was performed using the bifurcation method. It consists in determining the equilibrium positions of an elastic body, which differ little from the unperturbed state. By solving the linearized problem, the value of the external pressure at which the sphere first loses stability is found. The effect of dislocations on the buckling of thin and thick spherical shells is analyzed.

Minimization in incompressible nonlinear elasticity theory

1986 ◽  
Vol 16 (3) ◽  
pp. 267-301 ◽  
Author(s):  
R. L. Fosdick ◽  
G. P. MacSithigh
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Elasticity ◽  
Nonlinear Elasticity Theory ◽  
Incompressible Nonlinear Elasticity

Local solvability of a problem of nonlinear elasticity theory

1984 ◽  
Vol 25 (1) ◽  
pp. 918-926 ◽  
Author(s):  
V. G. Osmolovskii
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Elasticity ◽  
Local Solvability ◽  
Nonlinear Elasticity Theory

Hypoelastic form of equations in nonlinear elasticity theory

1974 ◽  
Vol 15 (2) ◽  
pp. 255-259 ◽  
Author(s):  
E. I. Romenskii
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Elasticity ◽  
Nonlinear Elasticity Theory
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