Stress analysis for a rectangular thick plate of a composite material with a spatially locally curved structure under forced vibration

Natural and forced vibrations of a thick rectangular plate fabricated from a composite material with a spatially locally curved structure are investigated with the use of exact three-dimensional equations of motion of the theory of elastic anisotropic bodies. The investigations are carried out within the framework of the continuum approach developed by Akbarov and Guz. It is supposed that the plate is clamped at all its edges and is loaded on the upper face with uniformly distributed normal forces periodically changing with time. The influence of the parameters of local curving on the fundamental frequency of the plate and on the distribution of the normal stress acting in the thickness direction under forced vibration is studied. The corresponding boundary-value problems are solved numerically by employing the three-dimensional FEM modelling.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 40, No. 6, pp. 779–790, November–December, 2004.     

Natural vibration of the beam-strip fabricated from a composite material with small-scale curvings in the structure

The frequency and forms of natural vibrations of a hinged beam-strip fabricated from a composite material with small-scale curved structures have been investigated using the plate theory in the framework of the Timoshenko hypothesis. The mechanical relationships of the composites are described by the Akbarov and Guz continuum theory. Using the corresponding variational principle, a method of solution of the considered problem is presented. Specific numerical investigations have been carried out for the case when the strip material consists of alternating equidistantly located and curved isotropic layers. The effect of existence of the curving in the beam-strip structure on its frequencies and forms of natural vibrations is studied. Cases of periodic and local curvings in the beam-strip material structure are considered separately.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Yilziz Technical University, Civil Engineering Faculty, 80750 Yildiz-Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 4, pp. 502–512, July–August, 1996.     

Three-dimensional analysis of stress fields in the plates fabricated from composite materials with small-scale structural curving

The stress distribution in plates fabricated from the multilayered composite materials with periodical smallscale curved structures has been studied. It is supposed that the continuously distributed normal forces act on the upper plane of the plate. Moreover, it is assumed that the plate is simply and rigidly supported at opposite sides. The investigation has been carried out in terms of the three-dimensional theory of elasticity, while the mechanical relationships of the given plate material have been described by the Akbarov and Guz' continuum approach. The numerical results obtained with the use of the seminalytical FEM show that the curving in the plate material structure affects the stress distributions in this plate.Chemical and Metallurgy Faculty, Department of Mechanical Engineering, Yildiz Technical University, 80750 Yildiz-Istanbul, Turkey. Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 3, pp. 340–348, May–June, 1997.     

Application of the finite-element method to improve the quasi-exact reinforcement theory of fibrous polymeric composites

In the paper, the WL quasi-exact reinforcement theory of fibrous polymeric composites is improved. An optimum compatibility condition related to the transverse shear problem for a unit cell, which brings solutions closest to reality, is derived. This condition is formulated in the form of a linear combination of maximum radial and circumferential displacements. Optimum coefficients of this combination are determined by comparing analytical and numerical solutions for a test specimen in the form of a rectangular thin plate, which is in a plane strain state and is subject to selected loading schemes. The analytic solutions are obtained for a homogenized material by using the WL reinforcement theory. The numerical solutions are found for an actual heterogeneous composite material by using the finite-element method, and they verify the WL reinforcement theory, in particular, the admissibility of Hills assumption. An analysis performed for two composite materials shows that the improved WL reinforcement theory gives adequate displacement fields.Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 79–92, January–Febrauary, 2005.     

Analysis of plates of polymeric material subjected to local loads

An approximate method of analyzing plates of polymeric material under local loading is described. The state of stress and strain and the stability of the plate are investigated.Moscow Institute of Electronic Machine Building. Translated from Mekhanika Polimerov, No. 3, pp. 430–434, May–June, 1976.     

Grapho-analytical method of calculating the deformation of a viscoelastic rod in axial tension under nonstationary temperature conditions

The strains in the material are calculated on the basis of a compound mechanical model consisting of a system of individual elastico-viscous models of the Maxwell type. This model makes it possible to allow for the time dependence of the temperatures and stresses in the cross sections of bodies of simple shape—rod, plate, thin-walled shell—and to calculate the strains under nonstationary temperature conditions from the creep curves for reinforced plastics with allowance for the previous loading history both under a constant load and for an arbitrary loading law.Mekhanika Polimerov, Vol. 2, No. 3, pp. 413–420, 1966     

Polymer fatigue from the standpoint of the kinetic theory of fracture

A comparison of the static and cyclic lives of various polymers shows that, whatever the loading regime, fracture may be regarded from the standpoint of the thermal-fluctuation theory. Under comparable test conditions the lifetimes in different loading regimes coincide. The experimentally observed cases of a reduced cyclic as compared with static life do not conflict with the kinetic theory of fracture and can be attributed to hysteresis heating effects or to differences in the structural changes that take place in the test material in different loading regimes.From the standpoint of the kinetic theory, fracture is regarded as a certain process that develops in a body under load and not as a critical event that occurs when a critical stress — ultimate strength — is reached.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 1, pp. 70–96, January–February, 1969.     

Quasilinear theory of viscoelasticity

By postulating equal contributions the number of kernels in the principal cubic theory of viscoelasticity and in the theory with regular kernels of two arguments is reduced to three. For certain quasilinear relations all the kernels and functions are determined from creep, relaxation, and simple loading and deformation tests. In the case of simple loading and deformation the problems for a viscoelastic incompressible material reduce to problems of the theory of small elastoplastic deformations of an incompressible material. Several problems relating to this case are considered.Moscow M. V. Lomonosov State University. Translated from Mekhanika Polimerov, No. 4, pp. 603–611, July–August, 1969.     

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.     

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.     

Relation between the vectors E and S for a plastic material in succesive biaxial tension

The local strains theory is used to determine the values of the components of the vector E{E₁, E₂} in five-dimensional space for a material subjected to successive biaxial tension at degrees of nonlinearity n=3 and n=5. The relation between the vectors E and S and the tangents to the loading and strain trajectories is considered together with the relation between the moduli E of the strains for simple and complex loading.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 975–979, November–December, 1969.     

Fibre stability in anisotropic matrix at small strains

As acknowledged in almost all monographs on the fracture of composite materials, one of the major fracture mechanism in unidirectional fibrous composites under uniaxial compression along the reinforcing elements is the stability loss of the material structure (the structural instability). According to this mechanism, theoretical investigations of the fracture along the fibres are reduced to those of the stability loss in the material structure, and the value of external critical forces is accepted as the value of failure forces. At present, numerous theoretical investigations have been carried out in this field with the use of the three-dimensional linearized theory of stability in the framework of the piecewise-homogeneous body model. However, in all the investigations it is assumed that the matrix and the fibre material are isotropic. It is evident that in many cases it is necessary to take into account the anisotropy of the matrix material when investigating the stability loss of fibres. In view of the above, in the framework of the piecewise-homogeneous body model using the three-dimensional linearized theory of stability, the present paper considers the stability loss of the fibre in the anisotropic (transversally isotropic) matrix. The effect of the properties of the matrix material on the critical values of the external loading is examined.Submitted to the 10th International Conference of Mechanics of Composite Materials (Riga, April 20–23, 1998).Published in Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 603–611. September–October, 1997.     

The elastoplastic stressed state of a half-plane under local nonstationary heating

We solve the thermoplastic problem for a semi-infinite plate under local nonstationary heating by heat sources. The physical equations are taken to be the relations of the nonisothermic theory of plastic flow associated with the Mises fluidity condition. The solution of the problem is constructed by the method of integral equations and the self-correcting method of sequential loading, where time is taken as the loading parameter. We carry out numerical computations of the stresses in the case of heating a plate with heat output by normal-circular heat sources. We study the problem of optimization of heating regimes in order to introduce favorable residual compressive stresses (from the point of view of hardness) in a given region of a half-plane. Two figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 29–34.     

Deformation and stress distribution in a layered plastic

The stress distribution over the unidirectionally reinforced layers is investigated in relation to the layer thickness ratio and the direction of loading of a two-way reinforced plastic. An expression is obtained for the modulus of elasticity of the layered plastic in an arbitrary direction relative to the directions of reinforcement. The effect of the geometry of the structure of the layered material on its deformation properties is experimentally illustrated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 563–570, May–June, 1972.     

Effect of combined loading on the components of the compliance tensor in shell stability problems

The local strains theory is used to establish relations for determining the components of the compliance tensor in shell buckling with allowance for combined loading of the material at the buckling point and as a function of the precritical loading path in stress space.Mekhanika Polimerov, Vol. 2, No. 3, pp. 387–391, 1966     

Complex loading of a polymer material with nonlinear creep

The nonlinear tensor stress, strain, and time relations for a memory-type medium under complex loading are examined using degenerate kernels. The basic expressions for simple loading and the material parameters were determined in [5]. The local strains theory is used to find expressions for the strain components in the presence of stepwise complex variation of the stress components, and these expressions are shown to be in satisfactory agreement with the experimental data for high-density polyethylene.Mekhanika Polimerov, Vol. 3, No. 3, pp. 421–426, 1967     

Evolution of the Stress–Strain State of a Three-Dimensional Plate Weakened by a Central Crack under Impulsive Tension

A method is developed to describe the formation of the stress–strain state in the vicinity of the tip of a stationary crack in a three-dimensional plate under dynamic loading. The energy model used to describe the formation of the stress concentration zone around the crack tip is modified to take into account the transient character of the loading process and the influence of the free surfaces of the plate on the stress–strain state of the central part of the sample. The method is useful for describing static and dynamic brittle fracture from a unified point of view.     

Action of a concentrated load on an elastic ring pressed into a circular hole in an anisotropic plate

A solution is obtained for the elastic equilibrium problem for an anisotropic plate with a circular hole into which is pressed a ring of arbitrary cross section symmetrical about the middle surface of the plate. Before deformation the outside radius of the ring differs from the radius of the hole in the plate by the amount of the permissible elastic displacements. A normal concentrated load is applied to the ring. The ring is analyzed in accordance with the theory of thin curved bars. A numerical example is given.I. Franko L'vov State University. Translated from Mekhanika Polimerov, No. 6, pp. 1054–1059, November–December, 1973.     

Bending features of a sandwich panel with asymmetric structure under local loads

The bending characteristics of a composite panel with asymmetric layered structure under local surface loads are obtained. A refined version of the applied theory is developed using the analytical solution of the bending problem of a sandwich plate with arbitrary asymmetric structure under a point load. Local effects are investigated within the limits of a discrete model allowing for the specific character of elastic properties of a soft filler. The advantages of the solution are expressions of bending characteristics — layer curvatures, displacements, and stresses — in a closed form. It is shown that these characteristics can vary several times depending on the asymmetry parameters of the structure. Degeneration peculiarities of the solution, stemming from the slipping of layers or, otherwise, their rigid linking by the Kirchoff—Love hypothesis, as well as from account of the transverse shear and compression of the normal, are examined in line with the degeneration of geometric and physical parameters of the discrete model adopted. The results obtained are illustrated by curves and surfaces for the characteristics studied.Submitted for the 11th International Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000).Institute of Polymer Mechanics, Latvian University, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 717–742, November–December, 1999.     

Quasilinearization method for coupled dynamic problems of thermoviscoelasticity

Use of the quasilinearization method is proposed for the solution of coupled dynamic (particularly, quasistatic) problems of thermoviscoelasticity under cyclic loading. The coupled problems under consideration here include vibrations of a one-dimensional body (beam, plate, shell) and shear vibrations of a hollow cylinder made of a material with temperature-dependent properties, with the principle of temperature-time analogy applicable in the latter case. The quasilinearization method is shown to be a fast converging one when applied to the solution of these problems.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 2, pp. 310–316, March–April, 1976.