Region of applicability of applied theories in problems of the stability of bars and plates with low shear stiffness subjected to uniaxial compression

The question of the region of applicability of applied theories of bending of bars and plates in stability problems is discussed in relation to the case of uniaxial compression. The critical loads given by these theories are compared with the recently obtained solution [4, 5, 7–10] based on the three-dimensional linearized equations of the theory of elasticity [6]. It is established that for the problems in question the Timoshenko and Ambartsumyan theories are accurate enough for engineering purposes over the entire practical region of variation of the geometric and physical parameters of the bar (plate), whereas the use of the Euler-Bernoulli and Kirchhoff-Love theories may lead to unacceptable errors.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga; Lvov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1124–1126, November–December, 1969.     

Stability of transversally isotropic shells coupled with an elastic foundation

The stability of shells coupled with an elastic Winkler foundation is investigated. It is assumed that the shell is made of a material (glass-reinforced plastic) with low resistance to shear, as a result of which generalized theories that take transverse shear strains into account [1–4] must be used in the stability calculations. The solution obtained is compared with the corresponding solution obtained on the basis of the classical Kirchhoff-Love theory [8].Lvov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 669–673, July–August, 1969.     

Construction of a phenomenological theory of fracture of anisotropic media

The theory of fracture proposed in [1] is extended to anisotropic media.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 634–644, July–August, 1971.     

Stability of shear-compliant cylindrical shells connected with an elastic foundation in a geometrically nonlinear formulation

The effect of transverse shear strains on the stability "in the large" of a cylindrical transversal-isotropic shell with an elastic filler under the effect of axial compression is investigated. The length of the cylindrical shell is assumed to be greater than the diameter. The approximate solution is obtained by the Bubnov-Galerkin method. Such a problem for an isotropic shell was considered earlier in [2, 4] on the basis of the equations of the classical Kirchhoff-Love theory.L'vov Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR. Ternopol Branch, L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 113–117, January–February, 1972.     

Bending of long rectangular plates with low shear strength

The bending of rectangular glass-reinforced plastic plates is investigated for various edge conditions on the basis of generalized applied theories of the Timoshenko and Ambartsumyan types [4]. A series of qualitative and quantitative differences is obtained as compared with the corresponding results of the classical Kirchhoff theory [1].L'vov Polytechnic Institute; Ivano-Frankovsk Institute of Oil and Gas; Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 945–950, September–October, 1969.     

Vibration of a viscoelastic rectangular orthotropic plate on a viscoelastic foundation

The integrodifferential equation describing the vibration of a viscoelastic rectangular orthotropic plate resting on a viscoelastic foundation with two foundation moduli is investigated. The solution of the starting equation is obtained by the method of straight lines [1] in conjunction with the averaging method [2]. By setting c₁=0 or c₂=0 or their combinations in the solutions obtained we obtain various particular cases that are generalized in the present investigation.Institute of Cybernetics and Computer Center, Academy of Sciences of the Uzbek SSR, Tashkent. Institute of Mechanics and Earthquake Resistance of Structures, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Mekhanika Polimerov, No. 6, pp. 1087–1094, November–December, 1970.     

Periodic deformation and viscous flow of polymer solutions and melts

The effect of nonlinear periodic deformation on the relaxation spectra and viscous-elastic characteristics of polymer melts and solutions is considered. The experimental and calculated relationships between the dynamic characteristics and effective viscosity and the amplitude of the rate of periodic deformation were compared.For Communication 1, see [6].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Institute of Mechanics Problems, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 357–366, March–April, 1970.     

Dynamic stability of an elastic orthotropic cylindrical shell with allowance for transverse shears

The resolvents for the dynamic stability of an elastic orthotropic cylindrical shell are obtained in accordance with the Ambartsumyan and Timoshenko-type refined theories. The regions of instability given by the classical and refined theories are compared. The dependence of the refinements on the shell parameters, the shear moduli of the material, and the buckling modes are investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 312–320, March–April, 1973.     

Effect of nature of metallic subs trate on adhesion strength of polyvinylbutyral - metal joints

The effect of the physicomechanical properties of the substrates on the adhesion strength of the metal—polymer system was investigated.Institute of the Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Institute of Chemistry and Chemical Technology, Academy of Sciences of the Lithuanian SSR, Vil'nyus. Translated from Mekhanika Polimerov, No. 1, pp. 81–86, January–February, 1972.     

Nonlinear creep in high-density polyethylene under time-dependent stresses

The authors have performed experiments on the creep of specimens of high-density poly-ethylene in states of plane stress which vary linearly with time. The theoretical curves are calculated from equations of two types, namely the cubic and principal cubic theories of viscoelasticity [3]. The parameters of the material are taken from a previous paper [1].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 796–803, September–October, 1973.     

Effect of material properties on the stability of transversely isotropic shells with an elastic filler subjected to the action of mechanical loads and temperature

The effect of the low shear strength of the material (glass-reinforced plastic) on the stability of cylindrical shells with an elastic filler is investigated in relation to axial compression, external pressure, and heating. The equations of the thermoelastic problem of the theory of monotropic shells, constructed with allowance for the effect of tangential shearing stresses, are used in the calculations.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Polytechnic Institute. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 903–907, September–October, 1970.     

Effect of material structure on the stability of a laminated-plastic cylindrical shell

A compact equation is proposed for analyzing the stability of layered shells in relation to their structure. The case of a shell with split longitudinal-transverse winding subjected to hydrostatic pressure is investigated.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 147–150, January–February, 1971.     

Stability of plastic plates and shells

Recent research on the stability of plastic plates and shells, mostly by workers in the Soviet Union, is briefly reviewed.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 5, No. 1, pp. 150–156, January–February, 1969.     

Resolvents of the theory of orthotropic shells with low shear stiffness in force-moments and stress functions

The problem of the theory of orthotropic layered shells with low shear stiffness is reformulated in force-moments and stress functions on the basis of new strain continuity relations constructed with allowance for transverse shears.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1970.     

Surface instability of high-elastic materials

The problem of the surface instability of a lower half-plane in compression is investigated for an arbitrary form of the potential within the framework of the plane problem of the deformational stability of incompressible elastic bodies at finite subcritical strains [1, 4]. Numerical examples are considered for high-elastic bodies with potentials of the Mooney and Treloar types.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 6, pp. 1107–1110, November–December, 1970.     

Concerning the investigation of the supermolecular structure of polymers with a three-dimensional network

The results of an investigation of the structure and properties of a series of crosslinked polymers are presented. It is shown that the structure is determined by the chemical structure of the starting components and the method of synthesis.Institute of Chemistry of High-Molecular Compounds, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 934–936, September–October, 1970.     

Problems of the theory of deformation of polymeric materials under complex loading

Research on problems of the theory of deformation of polymeric materials under complex loading based on a synthesis of creep theories and the local strains theory is reviewed.Presented at the 2nd All-Union Conference on Polymer Mechanics, Riga, November 10–12, 1971.M. V. Lomonosov Moscow State University. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 434–443, May–June, 1972.     

Periodic deformation and viscous flow of polymer solutions and melts

The transition from the start of deformation to the establishing of a stationary state of nonlinear, periodic shear deformation and the kinetics of the change in the mechanical characteristics after deformation at finite amplitudes has ceased have been investigated. The calculated values have been compared with those obtained experimentally.For Communication 2 see [3].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Institute of Mechanics Problems, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 3, pp. 521–529, May–June, 1970.     

Certain problems in developing a theory and design methods for anisotropic shells and plates with finite stiffness in shear. A survey

A survey is presented here of research on theory and design methods for shells and plates made of anisotropic materials, such as laminate reinforced plastics [4–13], compliant in shear. The report is based mainly on studies made at the Western Science Center, Academy of Sciences of the Ukrainian SSR during the last five years (after the previous survey [8] has been published), with the introduction of generalized Timoshenko-type theories.Branch of Mathematical Physics, Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 2, pp. 269–284, March–April, 1975.     

Evaluation of the surface tension of a fiber

Conclusions 1. The use of central-force theory in the calculations of molecular forces gives results analogous to those obtained using the usual theories of a surface layer in an artificial fiber.2. The surface layer of the models of a fiber chosen in this paper is characterized by an extensive force which is smaller in absolute value than the internal compressive forces.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 1, pp. 12–14, January–February, 1977.