Approximation of density of potentials for the flat viscoelastic bodies with inclusions, bounded by a piecewise smooth contours

An approach for approximating unknown densities of potentials in the study of the stressed state of a flat viscoelastic piecewise homogeneous body with inclusions, bounded by piecewise smooth contours, is proposed. The method is based on the construction of a system of boundary-time integral equations to determine the unknown densities of potentials along the contours of the inclusions. The approximation of the unknown densities of potentials was performed taking into account the singularity of the stressed state of a flat viscoelastic body near the angular point of the dividing line of the regions.

On internal stability loss of a row unidirected periodically located fibers in the visco-elastic matrix

In the present paper, the microbuckling or internal stability loss in the viscoelastic composites containing unidirected fibers under compression along the fibers is studied by use of piecewise homogeneous body model. In this model, it is used the 3-D geometrically non-linear exact equations of viscoelasticity theory. The composite material was considered as an infinite viscoelastic body with a row unidirected periodically located elastic fibers that have an initial infinitesimal imperfection. When the initial imperfection starts to increase and becomes indefinitely, this is taken as a stability loss criterion and co-phase microbuckling mode out of plane are taken into account. The numerical results about the influence of the interaction between the fibers on the values of the critical time are obtained and presented.

On Some Particularities of the Axisymmetric Wave Propagation in the Initially Twisted Circular Compound Cylinders

This paper investigates some particularities related with the influence of the magnitude of the initial twisting of the axisymmetric wave propagation in the initially twisted circular bi-material compounded cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic wave propagation in an initially stressed body. The mathematical formulation of the problem is presented and the corresponding solution method is proposed and developed. The numerical results are further presented and discussed. In particular, the mechanism of the arising of the new type modes caused by the initial twisting of the circular compounded cylinders is established.

Axisymmetric Wave Propagation in the Initially Twisted Circular Compound Cylinders

Within the scope of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic wave propagation in an initially stressed body, the problem of the axisymmetric wave propagation in an initially twisted circular compound cylinders is studied. The mathematical formulation of the problem is presented and the corresponding solution method is proposed and developed, following which the numerical results are presented and discussed. In particular, it is established that as a result of the initial twisting of the circular compound cylinders, new axisymmetric wave modes arise.

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.