S. D. Akbarov

The influence of the third order elastic constants to the generalized Rayleigh wave dispersion in a pre-stressed stratified half-plane

Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elasticity the influence of the third order elastic constants on the velocity of the generalized Rayleigh wave propagation in a pre-stressed stratified half-plane is investigated. Between the layer and half-plane the complete contact conditions are satisfied. The concrete numerical investigations are made on the various materials for which the values of the third order elastic constants are known. The initial stresses are determined within the framework of the classical linear theory of elasticity.

On the fracture of the unidirectional composites in compression

Abstract The experimental studies of the fracture of unidirectional composite materials under loading along the reinforcing elements showed that one of the major mechanism of this fracture is the stability loss in material structure. Up to the present time, numerous theoretical and experimental investigations of the mentioned problems have been made. Note that in these investigations (carried out from a theoretical viewpoint), the problems considered have been studied in the framework of the Euler approach and those have been reduced to investigations of the corresponding eigenvalue problems. In the present paper, a method for investigating the problem of fracture (stability loss) of a unidirectional composite in compression has been given, which uses as a criterion the value of the compressive force for which the initial infinitesimal curvature given to the fibre or layer starts to increase and grows indefinitely. In these cases the investigations are carried out in the framework of the piecewise-homogeneous body model with the use of the exact three-dimensional non-linear equations of the deformable solid body mechanics.Note that the results obtained with the application of the proposed approach to the investigation of the mentioned fracture problems coincide with those which have been obtained in the framework of the Euler approach. Moreover, the approach is also employed successfully for the theoretical investigations of the problems of the fracture mechanics of composites in compression, where the study in the framework of the Euler approach are impossible. In the present paper the fracture (stability) problems of composites with viscoelastic components in compression are also studied by the use of the proposed approach.

Mechanics of Curved Composites (Piecewise-Homogeneous Body Model)

A review is made of studies on the mechanics of curved composites carried out using the piecewise-homogeneous body model and the exact three-dimensional equations of the theory of elasticity and viscoelasticity. Relevant problem formulations and solution methods are considered and some typical results on the influence of structural distortion on the mechanical behavior of composites are analyzed. Subjects for near-term studies are proposed

A method of investigation of the general theory of stability problems on structural elements fabricated from viscoelastic composite materials

In the framework of the general theory of stability (GTS) the method for the investigation of the stability loss problems of the elements of constructions fabricated from the non-aging linear viscoelastic composite materials is proposed, with an example problem. The proposed approach is based on the investigation of the development of the initial insignificant imperfection of the considered elements of constructions in the framework of the geometrical non-linear exact equations of the deformable solid body mechanics. All investigations are carried out on the clamped strip. The numerical results (critical time) obtained in the framework of the proposed approach are compared with the numerical results found in the framework of the displacement based third order refined plate theory.

On the buckling of the elastic and viscoelastic composite circular thick plate with a penny-shaped crack

Buckling problem of the elastic and viscoelastic rotationally symmetric thick circular plate with a penny-shaped crack is investigated. It is supposed that the crack edges have a small initial rotationally symmetric imperfection. The lateral boundary of the plate is clamped and the clamp compresses this plate circumferentially and inwards by a fixed radial displacement. The investigations are carried out in the framework of the exact geometrically non-linear equations of the theory of viscoelasticity and as a buckling criterion the case for which the initial imperfection of the crack edges start to increase indefinitely is taken. Numerical results are obtained using the Laplace transform and finite element method and are compared with the known ones for elastic composites.

The effect of initial stresses on harmonic stress fields within the stratified half plane

The effect of initial stresses on dynamic (harmonic) stress fields within an elastic stratified half plane is investigated. It is assumed that the point-located harmonic force acting on the free plane of the layer by which the half plane is stratified causes this stress field. By employing displacement potentials and the exponential Fourier transform the governing system of partial differential equations of motion is solved. The necessary inverse transformations including rigorous mathematical complexity is performed numerically. The analysis of the numerical results, which shows the influence of the homogeneous initial stresses on the distribution of the stresses on the inter-medium plane, is made. These analyses are examined for various problem parameters and it is assumed that the material of both the layer and the half plane is homogeneous, isotropic, compressible and linearly elastic. It has been observed that the initial stresses may change significantly the values of the superimposed harmonic stresses.

Statics of laminated and fibrous composites with curved structures

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.

Mechanics of Curved Composites and Some Related Problems for Structral Members

ABSTRACT A review is made of investigations of the mechanics of curved composites. By curved composites we mean unidirectional fibrous and layered composites whose reinforcing fibers or layers have an initial curving or bending. The investigations carried out within the framework of the continuum theories and within the framework of the piecewise-homogeneous body model are considered separately. The corresponding theories, formulation of the problems, and solution methods for these problems are considered and some typical results on the influence of the curvature on the mechanical behavior of the composite are analyzed. Subjects for future investigations are presented.

On the Delamination of a Viscoelastic Composite Circular Plate

Delamination of a symmetric circular plate made of viscoelastic composite is studied. It is assumed that the plate has a penny-shaped crack whose edges have a minor axisymmetric imperfection. The lateral surface of the plate is clamped and is compressed by uniform radial normal forces through a rigid body. The studies are made using the exact geometrically nonlinear equations of the theory of viscoelasticity. The delamination criterion is assumed unrestrained growth of the initial imperfection. The Laplace transform and FEM are employed. In particular cases, the results are compared with those for elastic composites

On the bending problems of anisotropic (orthotropic) plates resting on elastic foundations that react in compression only

Abstract In several works, the bending of plates resting on elastic foundations that react in compression only have been investigated. In all of these investigations, the bending of the plates is described within the framework of Kirchhoff-Love hypothesis and the material of those plates are supposed to be isotropic. Therefore, the results of the above-mentioned investigations are not suitable for the bending of the plates fabricated from the composite materials and resting on the elastic foundation that react in compression only. In the present paper, the development of the solution method of the bending problems of the plates fabricated from the composite materials on the “tensionless” elastic foundation is proposed and the influence of the plate material properties to the displacement distribution and the form of the contact region is studied with concrete problems as an example. In this case, the plate material is modelled as an anisotropic material with the normalized mechanical properties; and the bending of the plate is described by using some version of the higher order refined plate theory. Moreover, with respect to the foundation, the following cases are considered; (1) Winkler foundation: (2) elastic half-space. 1997 Elsevier Science Ltd.