Elasticity Theory Method Research Articles

Specific features of the nonlinearly elastic behavior of cylindrical compressible bodies in torsion

The torsion problem of a cylinder with a circular transverse cross section twisted by end moments that are equal in magnitude and opposite in direction is considered for various models of nonlinearly elastic compressible media. The problem is solved by the semi-inverse method of elasticity theory. The Poynting effect, which consists of variation in the length of a shaft in torsion, is treated qualitatively and quantitatively. The results of the numerical and asymptotic (only terms that are quadratic relative to the displacement gradient are conserved) solutions for various models of the nonlinearly elastic behavior of materials are compared. An analysis of the results shows that in some cases, the quasilinear model is not applicable for studying the behavior of nonlinearly elastic compressible media.

Mathematical modeling of extension of an inhomogeneous elastic cloth

We propose mathematical models for a knitted fabric in tension that can be used to calculate the strain of the cloth thread from the properties of the cloth and the loads applied to the cloth. Under simplifying assumptions, the problem is reduced to consideration of an elementary cell of the cloth that contains a thread loop. The loop is first modeled by a thread oval with point forces and then by a plate with a hole under distributed loads. In strength analysis, this allows one to use methods of elasticity theory. A number of hypotheses are used to establish the relation between the stress state of the thread oval and the corresponding state of the plate, which makes it possible to model the mechanical behavior of a thread in the material in a variety of forms. The theoretical relationships obtained are compared to the experimental data available in the literature.

Simulation of the process of accumulation of substances near stress concentrators

In the framework of a model of an elastic deformable body, we analyze the phenomenon of accumulation of aggressive media near fibers and cracks in stressed materials. The fluxes of active elements in the material are specified according to the principles of nonequilibrium thermodynamics. By using the conditions of continuity of the indicated fluxes, we deduce a system of differential equations that takes into account the influence of mechanical and physical fields. By applying the methods of elasticity theory and linear fracture mechanics, we obtain the analytic dependence of the concentration of aggressive media near spherical cavities, fibers, and cracks on the stress intensity factors corresponding to the relevant local elastic fields.

Flat elasticity theory application for the description of stressed state and fracture of solids under phase transitions

The stress function is proved to be biharmonic for an elastically isotropic crystal undergoing phase transition which follows spontaneous dilatation. For an elastically anisotropic crystal which is neither improper nor proper ferroelastic, as well as for the improper ferroelastic, the stress function is proved to fulfil the Lehnitsky equation. The flat elasticity theory methods are extended to the case of crystals undergoing phase transitions. The stressed state, arising due to the phase transition in a crystal with a crack or with a rigid inclusion, is described. The spontaneous fracture conditions of crystals under phase transitions are obtained.

THEORY OF MAGNETOSTRICTION IN AMORPHOUS FERROMAGNETS

THEORY OF MAGNETOSTRICTION IN AMORPHOUS FERROMAGNETS

Strength of reinforced-concrete hydraulic structures having block joints

1. The proposed method of calculating the strength of reinforced-concrete structures permits taking into account the actual discontinuity of a massive structure (presence of block joints). 2. On the basis of a multiple-factor analysis of the state of stress obtained by the method of elasticity theory with the use of the theory of the strength of concrete, methods were proposed for calculating the crack resistance and predicting the failure of structures having block joints, which permit taking into account the nonlinearity of the distribution of stresses, combined stresses, and resistance of the principal longitudinal reinforcement to the effect of cleaving forces. 3. The results of the experimental investigations and the actual character of cracking of certain structures agree with the calculation results, which indicates the correctness of the initial assumptions of the proposed method.

On the error in determining the stress concentration at a free hole by plane elasticity theory methods: PMM vol. 32. no.6. 1968, pp. 1075–1083

On the error in determining the stress concentration at a free hole by plane elasticity theory methods: PMM vol. 32. no.6. 1968, pp. 1075–1083

Thermal stresses in reactor structures

The conditions in which thermal stresses develop in reactors are considered, their magnitude is estimated, and the extent of the danger they present. The influence of the shape of the fuel elements on the temperature gradient and on the magnitude of the thermal stresses is analysed; recommendations are made for decreasing the harmful influence of temperature stresses. The methods of elasticity theory used in the calculation of the thermal stresses have important limitations. In many eases, when one is estimating the size and extent of the danger arising from the thermal stresses superimposed on mechanical stresses and also in the search for measures to decrease them, one must take into account the additional influences of yield, creep, initial breakdown and of microscopic processes.