On the first boundary value problem for the classical theory of elasticity in a three-dimensional domain with a singular boundary

1973 ◽  
Vol 3 (4) ◽  
pp. 225-259 ◽  
Author(s):  
Pieranita Castellani Rizzonelli
Keyword(s):  
Boundary Value Problem ◽  
Classical Theory ◽  
Boundary Value ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Singular Boundary ◽  
Dimensional Domain

scholarly journals STABILITY OF A CYLINDER FROM MURNAGHAN MATERIAL UNDER STRETCHING, COMPRESSION AND INFLATION

2019 ◽  
Vol 81 (1) ◽  
pp. 30-39
Author(s):  
M. I. Karyakin ◽  
L. P. Obrezkov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Three Dimensional ◽  
Deformation Characteristic ◽  
Small Strain ◽  
Stability Loss ◽  
Theory Of Elasticity ◽  
Equilibrium Equations ◽  
The Stability ◽  
Loading Parameter

The problem of equilibrium and stability of a hollow cylinder subjected to simultaneous uniaxial tension/compression and inflation is considered within the framework of the three-dimensional nonlinear theory of elasticity. To describe the mechanical properties of the material of the cylinder five-constant Murnaghan model is used. By the semi-inverse method the three-dimensional problem is reduced to the study of a nonlinear boundary value problem for an ordinary second-order differential equation. For most sets of material parameters known from the literature, the presence of a falling section in the stretching/inflation diagram, indicating the possible existence of instability zones even in the area of tensile stresses, has been found numerically. The stability analysis was carried out using a bifurcation approach based on linearization of the equilibrium equations in the neighborhood of the constructed solution by means of the method of imposing a small strain on a finite one. The value of a particular deformation characteristic, for which non-trivial solutions of a homogeneous boundary-value problem exist for the equations of neutral equilibrium obtained in the linearization process, was identified with the critical value of the loading parameter, i.e. value at which the system loses stability. As a rule, the coefficient of stretching/shortening of the cylinder and the coefficient of increase/decrease of its internal or external radius were chosen as such parameters. On the plane of the above-mentioned deformation characteristics the areas of stability under tension and compression, as well as under compression by external force and inflation by internal pressure, are constructed. The forms of possible of stability loss depending on the type of stress state are constructed, and the effect on the stability of material and geometric parameters is studied.

On the Boundary Value Problem in A Dihedral Angle for Normally Hyperbolic Systems of First Order

1998 ◽  
Vol 5 (2) ◽  
pp. 121-138
Author(s):  
O. Jokhadze
Keyword(s):  
Partial Differential Equations ◽  
Boundary Value Problem ◽  
Principal Part ◽  
Hyperbolic Systems ◽  
Boundary Value ◽  
Three Dimensional ◽  
Order System ◽  
First Order ◽  
Dimensional Boundary ◽  
Class Of Functions

Abstract Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.

Sign in / Sign up

Export Citation Format

Share Document