теория упругости

Mode-Series Expansion of Solutions of Elasticity Problems for a Strip

Authors: Kossovich L. Y., Yurko V. A., Kirillova I. V.

Oscillations of a strip are considered as a plane problem of elasticity theory. Description of oscillation modes is provided. Properties of eigenvalues and eigenfunctions are studied for a boundary value problem for their amplitudes. Green’s function is constructed as a kernel of the inverse operator. Completeness and expansion theorems are proved which allow one to solve problems for finite and infinite membranes under arbitrary boundary conditions.

Mathematical Models of Stability Loss of Nonuniform Cylindrical Shells Because of Nonuniform Radial Loading

Authors: Antonenko N. N.

The circular cylindrical shell with variable thickness along the axis of elongation is considered. The axisymmetric radial pressure along the axis of shell is suggested. The one of values (for the law of pressure variation) which effects the stability loss of shell is determinated.

About Oblique Impact by Perfectly Rigid Body with Plane Boundary on the Nonlinear Elastic Half-Space

Authors: Dudko O. V., Potyanikhin D. A.

In this paper the impact interaction of perfectly rigid body and nonlinear elastic solid, which have plane boundaries, are investigated. Suppose that the moving rigid body has constant velocity, resulting in self-similar formulation of the problem. Possible variants of wave combinations, arising from such interaction, are discussed. The existence condition for evolutionary shock waves and the thermodynamic discontinuities compatibility condition serve as criterions for choosing the wave pattern.

The Parametric Oscillations of Heterogeneous Round Cylindrical Shell of Variable Density on Different Boundary Conditions

Authors: Mochalin A. A.

We consider an isotropic cylindrical shell of varying thickness and density along the generatrix. Let the shell be under pressure, which is symmetric and also varying along the generatrix. We follow the polupostamenty theory by V. Z. Vlasov and consider the problem of the dynamical stability of the shell. We obtain the exact solution corresponding to the certain relation between thickness, pressure and density.

Graph approach for finite-element based model of an elastic body under conditions of axisymmetric deformation

Authors: Tirimov A. A.

 A numerical method for analysis of the stress – strain state of elastic media based on a discrete model in form of directed graph is suggested. To analyze a deformable body using the graph approach, we partitione a solid body on elements and replace each element by its model in the form of an elementary cell. The matrices, presenting several structure elements of the graph, and the equations, describing the elementary cells, contribute to deriving the constitutive equations of the intact body.