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.     

On the applicability of two-dimensional applied theories to problems of the stability of axially loaded cylindrical shells made of materials with low shear stiffness

The applicability of two-dimensional applied theories of the Kirchhoff-Love, Timoshenko, and Ambartsumyan types to problems of the stability of shells with low shear stiffness [1] is discussed. The critical loads given by these theories are compared with those recently obtained [6–8] by solving the problem of the stability of a cylindrical shell on the basis of general solutions [3, 4] of the three-dimensional linearized equations of the theory of elasticity [5].Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. L'vov Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 141–143, January–February, 1970.     

Effect of material properties on the bending of cantilevered plates under a concentrated load

In a continuation of a previous study [4] a solution is obtained for the problem of a transversely isotropic plate in the form of an infinite strip bent by a concentrated load applied at an arbitrary point. The solution obtained is investigated in relation to the geometric and physicomechanical properties of the plate. The results are compared with the corresponding classical Kirchhoff solution [7].Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov; Kamenets-Podol'skii General Engineering Department of Khmel'nitskii Technological Institute. Translated from Mekhanika Polimerov, No. 4, pp. 704–707, July–August, 1971.     

Elastoplastic stability of glass-reinforced plastic plates with a central metal layer

The problem of the stability of a three-layer plate with a central plastic layer of metal sandwiched between elastic glass-reinforced plastic outer layers is considered. The presence of a metal layer restrains the development of creep strains in the glass-reinforced plastic and makes it possible to neglect the viscous strain components. The general equations of the problem are obtained, and the approximate Il'yushin formulation [1] is considered. An example is presented for a rectangular plate in pure shear. It is shown that the elastic anisotropic layers play the part of a load-relieving system for the central plastic layer [3], which results in an increase in the over-all critical load for the layered plate.Kalinin Polytechnic Institute. Translated from Mekhanika Polimerov, No. 5, pp. 909–915, September–October, 1969.     

Stability of glass-reinforced plastic plates resting on an elastic foundation

The stability of oriented glass-reinforced plastic plates resting on an elastic Winkler foundation is investigated using the theories of Timoshenko [2, 6] and Ambartsumyan [7], which permit the shear strains to be taken into account. The solution obtained is compared with the corresponding solution based on the classical Kirchhoff theory [8].L'vov Polytechnic Institute. Institute of Polymer Mechanics, AS LatSSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1082–1088, November–December, 1968.     

Experimental investigation of the transverse shear effect in the bending of cantilevered plates with low shear stiffness

The state of stress of cantilevered plates made of different materials (steel and glass-reinforced plastic) has been experimentally investigated. The results obtained are compared with the known theoretical solutions. It is shown that in certain cases it is necessary to take into account the effects associated with the low shear stiffness of the plate.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov; Kamenets-Podol'skii General Engineering Department of Khmel'nitskii Technological Institute. Translated from Mekhanika Polimerov, No. 4, pp. 736–738, July–August, 1971.     

A class of contact problems for thin anisotropic reinforced-plastic plates

Certain problems of the interaction of perfectly rigid smooth bodies and elastic reinforced-plastic plates are considered. The state of stress of the plate is described by the equations of orthotropic plates resisting interlaminar shear. Solutions are obtained in the case of a stamp in the shape of a rigid paraboloid of revolution indenting a circular plate with ring reinforcement and in the case of a parabolic cylinder indenting a unidirectionally reinforced plate in cylindrical bending. The expressions obtained for the contact pressure and the relation between the load P, the size of the contact region, and the settlement of the stamp are investigated with respect to their dependence on the orthotropy, wall thickness, and shear compliance parameters.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Ivano-Frankovskii Institute of Petroleum and Gas. Translated from Mekhanika Polimerov, No. 2, pp. 346–350, March–April, 1972.     

Effect of the properties of the material of the buckling of a plate

In [2] it was shown with reference to the cylindrical bending of a plate that the Kirchhoff-Love hypothesis is asympototically accurate for determining the critical load irrespective of the properties of the material. However, the question of the dependence of the critical load on the material properties was left unexplored. This question is now numerically investigated. Curves characterizing the variation of the critical load with relative shear modulus are presented.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 355–357. March–April, 1969.     

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.     

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.     

Effect of a local load on an orthotropic glass-reinforced plastic shell

The deformation of a layered orthotropic cylindrical shell under a local normal load is investigated on the basis of equations that do not depend on the hypothesis of straight normals. The solutions of the analogous classical problems were analyzed in [3]; a solution based on equations that take transverse shear strains approximately into account was proposed in [4]. The high degree of variability of the state of stress created by local loads indicates that it is quite important to take transverse shear strains rigorously into account in problems of this class. An attempt is made to estimate the error introduced by the hypothesis of straight normals and to calculate the load leading to debonding of the shell.S. Ordzhonikidze Moscow Aviation Institute. Translated from Mekhanika Polimerov, No. 1, pp. 95–101, January–February, 1970.     

Mechanism of failure of reinforced beams in bending

The mechanism of shear failure is investigated. A theoretical analysis makes it possible to determine the limits of shear failure of reinforced beams in relation to the geometric parameters of the beam, the mechanical properties of the reinforcement and the resin, their volume content, and the loading and support conditions. The results obtained are consistent with the experimental data of [1]. It is shown that in the process of shear failure the axial displacement distribution is modified and that the shear failure mechanism depends on the type of loading and the support conditions.Institute of Hydrodynamics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekahnika Polimerov, No. 4, pp. 698–709, July–August, 1973.     

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 a thin cantilevered orthotropic plate with a concentrated load at the free edge

The problem of a thin rectangular cantilevered plate of constant thickness with a concentrated load in the center of the free edge is considered. The plate is assumed to be orthotropic, the fixed edge coinciding with the principal direction of elasticity. An equation is obtained for the normal stresses at an arbitrary point on the plate. The theoretical results are compared with experiment.A. A. Zhdanov Gor'kii Polytechnic Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 739–741, July–August, 1968.     

Variation of the deformation resistance of phenol-formaldehyde thermosets during cure

The dependence of the viscosity of phenol-formaldehyde thermosets on the previous thermal history has been investigated at a fixed shear rate.Moscow Institute of Chemical Machine Building. Institute of Problems of Mechanics, Academy of Sciences of the USSR, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 619–623, July–August, 1971.     

Dynamic bending of plates with low shear strength

The dynamic problem of the natural vibrations of glass-reinforced plastic plates with low shear strength is examined. The calculations are based on the Timoshenko model (allowance for shear strains and rotational inertia). It is shown that disregarding effects associated with the large shear compliance of glass-reinforced plastic plates leads to appreciable errors in determining the dynamic characteristics.Institute of Polymer Mechanics, Academy of Sciencies of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 4, pp. 698–704, July–August, 1968.     

Influence of temperature and humidity on the creep of polymer materials

Conclusions By analyzing the results of the original creep tests under shear and tensile conditions subject to various temperatures and humidities, and also analyzing some control experiments involving simultaneous shear and tensile strain, we have shown that the displacement function of the relaxation spectrum expressing the maintenance of the temperature-humidity-time analogy is independent of the form of the stressed state in the range of linear viscoelasticity for a Poisson coefficient close to 0.5.For Communication 2 see [2].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 627–632, July–August, 1976.     

Thixotropy of filled-polyethylene melts subjected to periodic shear deformation

As a result of the action of periodic finite-amplitude shear deformations filled high-pressure polyethylene melts exhibit thixotropic properties. The effect of the previous deformation history on the frequency dependence of the complex dynamic shear modulus is investigated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR Riga. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 927–931, September–October, 1968.     

Stability of transversely isotropic annular plates with low shear resistance

The stability differential equations of a cylindrically orthotropic circular plate are obtained on the assumption of an axisymmetric buckling mode with allowance for transverse shears. These equations are solved for the case of a transversely isotropic material when the inner and outer edges of the plate are identically loaded by uniformly distributed radial forces. The transcendental equations for the critical load parameter are constructed for various edge conditions. The dependence of this parameter on the boundary conditions and the relative thickness of the plate, Poisson's ratio, and the ratio of the Young's and shear moduli of the material are investigated. Certain conclusions are reached concerning the design of reinforced-plastic plates.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 872–880, September–October, 1969.     

Stability of glass-reinforced plastic columns

The stability of circular columns of unidirectional glass-reinforced plastic (EF-32-301) is investigated for two types of end conditions: hinged at both ends and one end hinged, the other fixed. The experimental data are compared with theory [1]. A relationship is established between the change in reduced length and the shear parameter.Institute of Hydrodynamics, Siberian Branch, Academy of Sciences of the USSR, Novosibirsk. Translated from Mekhanika Polimerov, Vol. 4, No. 5, pp. 906–910, September–October, 1968.