Compliance tensor for an elastic material reinforced in two directions

The relations for all the independent components of the elastic compliance and stiffness tensors of an elastic material reinforced in two directions are examined on the assumption that it is a continuous, macroscopically homogeneous, anisotropic (orthotropic) medium. The results obtained are used to construct illustrative curves and are compared with certain experimental data.Mekhanika Polimerov, Vol. 2, No. 3, pp. 372–379, 1966     

Elastic constants of randomly reinforced plastics

A previously developed [4] general method of solving the nonlinear (in the statistical sense) boundary value problem of the theory of elasticity is used to determine the macroscopic moduli of elasticity of randomly reinforced plastics whose structure is simulated by a two-phase microinhomogeneous medium. The macroscopic modulus is represented in the form of a series composed of the sum of the mean value of the modulus and a sequence of corrections that take into account the central moments of the distribution of elastic constants. The limits of convergence of this series are established. The values of the macroscopic moduli for a glass-reinforced plastic obtained by calculation are compared with the experimental data.Mekhanika Polimerov, Vol. 3, No. 2, pp. 259–265, 1967     

Bloch constants for planar harmonic mappings

We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic functions as a special case. Also, for bounded planar harmonic mappings, we obtain results similar to a theorem of Landau on bounded holomorphic functions.

     

On the Koebe and Bieberbach constants for a hyperbolic planar domain

We discuss domain constants related to the classical Bieberbach and Koebe theorems. We find a class of simply connected domains for which the value of these constants is extremal and investigate the relationship between the geometry of a sequence of hyperbolic domains and the associated sequence of domain constants.     

Estimates on Bloch constants for planar harmonic mappings

The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan. This work was supported by the Research Foundation for Doctor Programme (Grant No. 20050574002) and the National Natural Science Foundation of China (Grant No. 10471048)     

Estimates on Bloch constants for planar harmonic mappings

The Schwarz lemma and Bloch constants for planar bounded harmonic mappings are considered. Sharper form and better estimates are obtained. Our results improve the one made by Dorff and Nowak as well as by Chen, Gauthier and Hengartner.     

Estimates for lebesgue constants in dimension two

Summary Let D denote the interior of a piecewise regular curve of R² having a point with Gauss curvature different from zero. We show that the Lebesgue constants L ^D relative to D behave like ^1/2 as .     

Thermoelastic problem for a circular cylinder of reinforced multilayer material

The temperature stresses and displacements are determined in an elastic circular cylinder of reinforced multilayer material. The relationship between the displacements of the inside and outside surfaces of the cylinder and the radial stresses and the mechanical and thermophysical properties of the components, the reinforcement ratio, and the ratio of the radii is investigated. The results are used to interpret the behavior of wound glass-reinforced plastic products under varying temperature conditions and during the curing stage.Mekhanika Polimerov, Vol. 3, No. 1, pp. 136–141, 1967     

Exact transient analysis of a planar random motion with three directions

Consider a planar random motion with constant velocity and three directions forming the angles ~ /6, 5 ~ /6 and 3 ~ /2 with the x -axis, such that the random times between consecutive changes of direction perform an alternating renewal process. We obtain the probability law of the bidimensional stochastic process which describes location and direction of the motion. In the Markovian case when the random times between consecutive changes of direction are exponentially distributed, the transition densities of the motion are explicitly given. These are expressed in term of a suitable modified two-index Bessel function.     

Experimental evaluation of the effect of prestressing the fibers in two directions on certain elastic characteristic of woven-glass reinforced plastics

The effect of prestressing the reinforcing fibers in either of two mutually perpendicular directions on the elastic characteristics of woven-glass reinforced plastics has been experimentally investigated. It is shown that an increase in the elastic characteristics in the prestress direction is accompanied by a decrease in the direction at right angles. Applying the same prestress in both directions considerably improves the moduli of elasticity (E_x, E_y). The possibility of using Bolotin's theory [1] and the relations proposed in [4, 6] to estimate the effect of regular distortions of the fibers on the elastic moduli of woven-glass reinforced materials is examined.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 859–863, September–October, 1968.     

Seshadri constants in two half-periods

We calculate the exact value of the multiple point Seshadri constant in two halfperiods of an abelian surface with Picard number one. Received: 3 December 2003; revised: 9 July 2005     

Reliability of multilayer plastics reinforced in three directions in a two-dimensional random stressed state

Conclusion The method developed permits considering the random character of the components of an applied stressed state and makes it possible to analytically predict the reliability of a three-directional LRP. The possibility of optimization of the material was demonstrated and the corresponding method was developed based on an analysis of the effect of the structure (geometry of the structure of the RES, number of layers), scattering of the loading and strength parameters on the reliability of LRP. The criterion for optimization of the structure of LRP in application to the actual conditions of random loading can be used both for a given loading level and for a required reliability level. Use of the method developed can also be promising in the case of the effect of combined loads.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1037–1045, November–December, 1989.     

Elastic characteristics of a cement-based composite reinforced with steel grid ribbons

A method is proposed for the estimation of elastic characteristics of a cement mortar orthogonally reinforced with punched steel grid ribbons. The method proposed takes into account the geometry of grids, the distance between ribbons, and the elastic properties of cement mortar and steel.     

Elastic characteristics of a cement-based composite reinforced with steel grid ribbons

A method is proposed for the estimation of elastic characteristics of a cement mortar orthogonally reinforced with punched steel grid ribbons. The method proposed takes into account the geometry of grids, the distance between ribbons, and the elastic properties of cement mortar and steel.Riga Technical University, Riga, LV-1047 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 173–180, March–April, 1999.     

Compliance tensor for an elastic material reinforced in one direction

An analysis of the way in which the components of a reinforced body work together is used to derive formulas for determining the components of the compliance and stiffness tensors for an elastic material (regarded as an anisotropic body) reinforced in one direction by elastic rods.Mekhanika Polimerov, Vol. 1, No. 4, pp. 52–59, 1965     

Particular case of twinning in a planar nine-atom model

The twinning curve of a planar nine-atom model under unsymmetrical loading has been calculated. The equilibrium forms of the model under compression were determined.