State of stress of flexible plastic shells with an opening

The state of stress of flat flexible shells with an opening is investigated with allowance for the viscoelastic properties of the material. The equilibrium equations and boundary conditions are written in finite-difference form. A nonlinear system of algebraic equations is solved by successive approximations. A method of accelerating the convergence of slowly converging iteration processes is proposed. The effect of the viscoelastic properties of the shell material on its state of stress is investigated with reference to the example of a polymethyl methacrylate shell. The variations of the ring moment and ring forces at the free edge of the shell are plotted for various moments of time, load values, and flatness parameters. It is shown that as soon as the viscosity factor begins to take effect, the state of stress and strain of the shell changes sharply; the concentration of forces and moments increases in the flexible viscoelastic (as compared with the elastic) shell.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1071–1075, November–December, 1973.     

Anisotropic ring stretched by rigid half-disks

A theoretical basis is provided for the experimental method of determining the elastic and strength properties of materials by stretching ring specimens with a pair of rigid half-disks. The equilibrium equations of the plane problem for an anisotropic ring with mixed boundary conditions are solved by means of an expansion in Fourier series with respect to the circumferential coordinate. Numerical results obtained on a computer are analyzed. The dependence of the circumferential stress concentration coefficient on various parameters is investigated.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1113–1116, November–December, 1970.     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

Bending of a cantilevered glass-reinforced plastic cylindrical shell weakened by a circular opening

The stress concentration is investigated in the neighborhood of a circular opening in a cantilevered glass-reinforced plastic cylindrical shell with a concentrated load at the free end. The problem is solved by the Bubnov method using a Ural-2 computer. The theoretical results have been checked experimentally on glass-reinforced plastic shells.All-Union Correspondence Polytechnic Institute, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 152–157, January–February, 1970.     

Flexure of viscoelastic plate with holes reinforced by rigid rings

The problem of the flexure of an Isotropic viscoelastic plate with three unequal circular holes reinforced by rigid rings is solved. The influence of the viscoelastic properties of the material on the stress state of the plate as a function of the distance between the holes and their radii is investigated.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 56–58, 1987.     

Finite-difference method of solving the bending problem for glass-reinforced plastic plates with allowance for creep

A new finite-difference method is proposed for solving the bending problem as it applies to thin rectangular orthotropic plates of linear hereditary material. The proposed method makes it possible to obtain a closed approximate solution in explicit form for a series of finite-difference systems of equations corresponding to the problem of the bending of plates of orthotropic glass-reinforced plastic with allowance for the rheological properties of the material under various boundary conditions.Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 6, pp. 1075–1082, November–December, 1969.     

Variation of certain transverse characteristics over the thickness of wound glass-reinforced plastic rings

The variation of certain transverse characteristics over the thickness of wound glass-reinforced plastic rings has been experimentally determined under normal conditions and at the polymerization temperature of the material investigated. The characteristics in question are used in investigating the state of stress of the ring and the initial fabrication stresses.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 165–167, January–February, 1970.     

Stresses in an anisotropic ring with moduli of elasticity varying along the radius subjected to internal and external pressure

The effect of nonuniformity of the elastic properties on the state of stress of an orthotropic ring subjected to pressure has been theoretically investigated. The results of the numerical calculations show that the effect of the variability of the circumferential modulus is more important.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1128–1130, November–December, 1971.     

State of stress of a hollow viscoelastic cylinder whose material properties depend on temperature

The state of stress of a long thick viscoelastic cylinder enclosed in an elastic shell is examined. The inner boundary recedes; body forces, internal pressure, and a uniform nonstationary temperature field are considered. The material properties depend on temperature; time-temperature superposition does not hold. A singular kernel is taken as the influence function. An approximate solution is found in displacements and stresses. A numerical example is presented.M. V. Lomonosov, Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 86–94, January–February, 1970.     

Basis of a test procedure for anisotropic annular samples

The mixed boundary problem for an anisotropic ring loaded by semidiscs or semirings is discussed. A numerical analysis of the solution is given. The results can be used for evaluating results of tests on annular samples manufactured from anisotropic materials.Moscow Energy Institute. Translated from Mekhanika Polimerov, No. 1, pp. 171–175, January–February, 1972.     

Effective elastic properties of particulate-reinforced compossite materials

A numerical approach for determination of the effective properties of particulate composite materials has been developed. A representative volume element (RVE) of the composite material is analyzed with help of the finite-element method. Uniform boundary displacements or tractions are applied on the boundaries of the RVE for introducing the known average strain in the RVE. Local stress and strain distributions in the RVE are calculated using the finite-element method. Different effective elastic constants can be calculated by averaging the local fields corresponding to different sets of boundary conditions. The present approach allows us to determine the effective properties of particle-reinforced composites with acceptable accuracy. The calculated effective properties of the composite are between the upper and lower Hashin—Shtrikman bounds. The results based on the present approach lead to higher stiffness of composites in comparison with analytical approaches.Institute fur Werkstoffwissenschaften, Fachberech Werkseoffwissenschaften, Martin-Luther-Universität Halle-Wittenberg, D-06099 Halle, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 450–459, July–August, 1997.     

Method of the anisotropy potential in the linear mechanics of polymers

The potential of the displacements due to the anisotropy of the physical properties of a material (the anisotropy potential) is used in order to reduce the solution of the linear statistical boundary problem of elasticity theory and that of the linear creep of homogeneous anisotropic bodies to two simpler problems: one involving an anisotropic medium, and the other involving an equation analogous to the Poisson equation.S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 1, pp. 24–31, January–February, 1972.     

Bending of a nonlinear orthotropic cantilever beam

The method of elastic solutions is employed to investigate the plane problem of the deformation of a cantilever beam of orthotropic glass-reinforced plastic under a concentrated load with allowance for the non-linear properties of the material. The first approximation of the stress function is given and the stress distribution over the cross section is calculated for a specific GRP.Mekhanika Polimerov, Vol. 2, No. 5, pp. 773–778, 1966     

Thermoelastic stresses in a nonuniform orthotropic cylinder

The stress distribution in a cylinder with cooling nonuniform with respect to the circumferential coordinate is investigated. The nonuniformity of the mechanical properties of the material in this direction is taken into account. Numerical results obtained at values of the parameters characteristic of wound glass-reinforced products are discussed.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 3, pp. 560–563, May–June, 1975.     

Reflection and transmission of sound waves through the interfacial boundary of two joined elastic half-strips

A numerical solution of the problem of the incidence of plane harmonic waves on the interfacial boundary of two joined half-strips with different elastic properties is presented. A detailed analysis is given of the reflection and transmission of the incident wave energy through the inter-facial boundary, and the nature of the state of stress and strain is investigated in its neighbourhood. The wave fields in longitudinally inhomogeneous media were studied earlier in /1–3/ etc.     

Stresses in an anisotropic cylinder

The present article considers the use of the random anisotropy potential to investigate the stress field in an anisotropic cylinder. The mechanical properties of the body are considered to be determined and the displacements at the boundary to be random. The general solution to the elasticity-theory problem for the displacements in an anisotropic body is expressed in the form of the sum of the general solution of a homogeneous equation system and the special solution of an inhomogeneous system. Determination of the latter reduces to solution of a system of integral equations with a common kernel in the form of Green functions of the Laplacian. The first- and second-order moments for the displacements and stresses are given, a numerical example is examined, and the convergence of the approximation-calculation procedure is investigated.S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No. 2, pp. 315–320, March–April, 1972.     

Structural Modeling of the Mechanical Behavior of Periodic Cellular Solids: Open-Cell Structures

The numerical simulation of random cellular metals, e.g., metal foams, is still connected with many unsolved problems due to their stochastic structure. Therefore, a periodic model of cellular metals is developed and its mechanical behavior is investigated numerically under uniaxial and multiaxial stress states. The main advantage of the model is that a wide range of relative densities can be covered and that test specimens of the same geometry are possible to manufacture without oversimplifying their shape. The influence of different hardening behavior and different boundary conditions on the characteristics of the material is investigated. Furthermore, the effect of internal pore pressure on its uniaxial behavior and on the shape of yield surface are determined.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 3, pp. 405–422, May–June, 2005.     

Extension of a piezoceramic bimorph with a crack crossing the interface

We consider the boundary-value problem of electroelasticity for a composite plate weakened by a crack crossing the line joining the media. The initial boundary-value problem, is reduced to a mixed system of singular integral and algebraic equations. We present the calculation results characterizing the variation in the stress intensity factors as a function of the opening angle of a segmented crack for different types of loading.Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 4, pp. 482–488, July–August 1997.     

Action of a shear stress pulse on the surface of a viscoelastic anisotropic half-space

The boundary value problem of the behavior of a viscoelastic half-space subjected to a surface shear stress pulse is solved in the linear formulation on the basis of dynamical correspondence principle. The medium occupying the half-space possesses the property of transverse isotropy. The exact solution of the problem is obtained using integral transforms. The solution is analyzed with reference to a Maxwell-Voigt model.Moscow Region. Translated from Mekhanika Polimerov, No. 5, pp. 933–937, September–October, 1969.     

Integral representation of an analytic function in a ring and its applications

An integral representation of an analytic function in a ring with corresponding limit values on the boundary is obtained. A new singular integral equation is suggested and solved in quadratures by using an integral representation and by complete investigation of the Cárleman problem for a ring (in the normal case).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 322–329, March, 1995.