Issue 3

JTAM, Sofia, vol. 2 Issue 3 (1971)

Axially Symmetric Creep Buckling of an Anisotropic Circular Cylindrical Shell Subjected to Axial Compression

M. Kozarov, R. Kurkchiev

An approximate solution of the problem of the creep buckling of an anisotropic circular cylindrical shell is given in the analysis. The shell is subjected to an axial compression load with total magnitude P. Very long shells are considered. In such case the effect of the supports can be neglected. Non-linear secondary creep is supposed. The creep law for the anisotropic material used in the article is a generalization of the Odquist’s creep law for isotropic bodies. As a result a simple formula for the critical time is deduced.

JTAM, Sofia, vol. 2 Issue 3 pp. 009-020 (1971)

Some Sufficient Conditions for Assymptotic Stability of a Neutral Type Equations System

V Diamandiev, Z. Zapryanov

The authors consider the conditions for an assymptotic stability of the system
(1)             x(t)=f[t, x(t), x(t-t(t)), x(t-t(t))].
For all systems (1), provided the condition of co-ordination is accomplished the following theorem is proved: the trivial solution of (1) is assymptotically stable if a definitely positive functional V[x(s), x(s),t] exists, assuming an infinitesimal upper limit, and having a non positive derivative lim dV/dt ≤ 0, whereupon the multiplicity of points at which lim dV/dt = 0 does not contain whole trajectory, with an exception of x = 0. It is assumed that the right parts fi of Eq. (1) are periodic with regard to t or they do not depend on t, and that their derivatives to the rest arguments are limited, as ∥∂f/(∂ x(t-t(t)))∥ ≦ a < 1. The first derivatives of the initial functions φ(s) for (1) satisfy the condition of Lipschitz. This condition is not necessary if there is a functional V[x(s),t].

JTAM, Sofia, vol. 2 Issue 3 pp. 021-028 (1971)

Bending of Slope Orthotropic Shells with Variable Thickness at Defining the Transversal Angular Strains

M.G. Kolchakov

The bending of slope orthotropic shells with variable thickness set on rectangular basis subjected to arbitrary orientated and distributed loadings and to a stationary temperature field, is considered at different boundary conditions. A specified shell theory which allows to define the effect of the transversal angular strains, respectively the transversal sliding strains on the stressed and strained state of the shell in dependence on its geometric characteristics and the physical parameters of the material from which it is made, is used. Several particular cases are considered.

JTAM, Sofia, vol. 2 Issue 3 pp. 029-040 (1971)

Thermodynamic Aspects of the Process of Microdestruction of Polymer Materials

A. Baltov

The process of microdestruction of polymer materials by means of the model of a body with internal parameters of state and the non-linear thermodynamic of the irreversible processes, is investigated. The process of microdestruction is considered as complex, consisting of mutually connected mechanic, thermal and diffusion-chemical processes. The basic system of equations describing the process is deduced, which makes possible the setting of purposeful experiments and the solution of concrete initially-boundary problems.

JTAM, Sofia, vol. 2 Issue 3 pp. 041-052 (1971)

Stress and Strain State of a Short Uniliterally Fixed Elasto-Plastic Cylindrical Shell

M. Mitov

A short cylindrical shell of elasto-plastic material with non-linear reinforcing is considered. The shell is fixed in one of its ends freely supported in tire other and loaded with uniformly distributed internal stress. D. Kolarov’s method for the softened physical equations is applied, proceeding from the theory of the small elasto-plastic deformation equations. The proposed method of solution is illustrated with numerical example and graphs.

JTAM, Sofia, vol. 2 Issue 3 pp. 053-062 (1971)

To the Analysis of the Problem for the Dynamic Interaction of a Circular-Cylindrical Shell with Ideal Liquid

Y. Djupanov

The speed potential of a layer of flexible liquid is determined by expanding the variation forms to eigenfunctions of the boundary problem of the liquid. The obtained solution, the mechanism of transition through the resonance zones, the energetic cycle shell-liquid-shell, the satisfaction of the initial conditions and other aspects of the problem are analyzed.

JTAM, Sofia, vol. 2 Issue 3 pp. 063-072 (1971)

Elastic Waves in an Elliptical Cylinder with Micropolar Structure

Ts. P. Ivanov

The propagation of harmonic waves in an infinite cylinder with elliptical cross section is considered on the basis of micropolar theory of elasticity. The solution of the problem is reduced to the solution of Mathieu’s equations by means of introduction of potential functions and separation of the variables. The boundary condition that the cylindrical surface is stressfree is obtained in the form of an infinite determinant permitting the determination of the phase velocities of wave propagation. The derived results allow the obtaining of particular case of harmonic wave propagation in circular cylinder.

JTAM, Sofia, vol. 2 Issue 3 pp. 073-081 (1971), [Full Article]