Isotropic and anisotropic elastic scatterers of underwater sound

Object and purpose of research. This paper discusses diffraction parameters of isotropic and anisotropic elastic scatterers, demonstrating that transversally isotropic bodies with a certain orientation of their planes of isotropy might be regarded as isotropic scatterers with similar size, shape and physical parameters. Materials and methods. Diffraction theory methods in solution of boundary problems and equations of dynamic elasticity theory for isotropic and anisotropic bodies. Main results. Calculation of moduli for angular parameters, as well as of relative back-scattering sections for isotropic and anisotropic scatterers of various shapes. Conclusion. The studies demonstrated that if transversally isotropic bodies of various shapes have a certain orientation of their planes of isotropy and a certain vector of a plane wave falling onto them, their reflection parameters, like relative backscattering sections and angular scattering characteristic of an anisotropic body are the same as those for isotropic bodies of similar size, shape and elasticity.

PROBLEM OF THE ANISOTROPY OF ELASTICITY AND STRENGTH IN ANISOTROPIC FIBER MATERIALS

Introduction: The paper presents new results of studies on the anisotropy of fiber materials with cylindrical anisotropy, which include filament-wound composite materials reinforced with various fibers. Methods: We suggest a mathematical solution to a fourth-order partial differential equation in polar coordinates with two variables for an orthotropic anisotropic body. To solve this equation, we converted it into Cartesian coordinates and presented the stress function as a sum of polynomials. Results and Discussion: As a result of the solution, we obtained two relationships between the elastic constants in the principal directions of anisotropy (so-called elasticity parameters). One of them was obtained for the first time, and the other results from the solution of the anisotropy problem for an orthotropic curved body, suggested by S. G. Lekhnitsky. The obtained solution does not contradict Lekhnitsky’s solution. Thus, in our opinion, orthotropic materials can be divided into two groups. In one group, when shifting from the radial to the tangential direction, the elastic constants take on extreme values when the layers are at angles of 0, 60, and 90°. In the other group, there is no intermediate extreme value and the elastic constants take on extreme values when the layers are at angles of 0 and 90°. The obtained results can be applied in the development of new high-strength composite materials and new technologies for the design and manufacture of building structures, as well as in the design of high-strength structures from synthetic composite materials.

Stressed state of two-layer strip when interacting with rigid base

Relevance. In the calculation of multilayer bases, when the material of one or several layers has a pronounced anisotropy, the nature of the distribution of displacements and stresses depends on the direction of the anisotropy axes in each layer. Therefore, it is necessary to have an evaluation of the influence of this factor in the design and analysis of the operation of multilayer media. The aim of the work - to research the stress state in a strip composed of two anisotropic plane-parallel layers with different physical characteristics, lying without friction on a rigid base. Methods. The integration of the equations of the plane problem of the theory of elasticity of an anisotropic body is carried out by the symbolic method in combination with the method of initial functions. The initial functions on the contact line of the strip and the base are determined from the conditions of tight adhesion between the layers, the conditions of tight contact and the absence of friction between the strip and the base, the nature of the load applied to the upper plane of the strip. After transformations, the functions of displacements and stresses in each layer are written through the normal surface load in the form of improper integrals. Results. Plots of changes in stresses in the strip from the values of the characteristics of anisotropic materials, layer thicknesses are given. The maximum stresses on the interface line of the layers and on the line of contact with the base, depending on the direction of the anisotropy axes in each layer, are presented in the tables and shown in graphs. The effect of the elastic modules of materials on the nature of the stress distribution in a strip composed of two isotropic materials is estimated.

Effect of friction in the interaction of an anisotropic strip with a rigid base

Relevance. Different models of contact between bodies are used in determining the stressed and deformed state in the strip lying on the base. It is necessary to evaluate the qualitative and quantitative nature of the change in stress in the strip depending on the coupling of the strip and base. The aim of the work - to analyze the effect of the coefficient of friction on the value of stresses in an anisotropic band when interacting with a rigid base. Methods. The solution is based on the equations of the plane problem of the theory of elasticity of an anisotropic body under the conditions that the band is closely adjacent to the base and the tangent force on the contact plane is proportional to the normal pressure. Displacements and stresses at any point of the strip are written in the form of the method of initial functions through the functions of displacements and forces on the lower plane, which depend on the nature of the load applied on the upper plane and the conditions of contact between the strip and the base. After the transformations, the calculation formulas for displacements and stresses are expressed using the Fourier integral transform through the normal surface load in the form of improper integrals. Results. Formulas for determining displacements and stresses are obtained for the variant of loading a strip with a concentrated force. These formulas are used to construct influence functions for the problem of equilibrium of an anisotropic strip lying on a rigid base, taking into account friction. Graphs of the effect of the coefficient of friction and the direction of the anisotropy axes of the material on the stress state of the strip are presented. The results of stress calculation are compared using anisotropic and isotropic models.

Numerical modeling of nanobundle- and nanorope- reinforced polymer mechanical properties

Carbon nanotubes (CNTs) demonstrate unusually high stiffness, strength and resilience, and are ideal reinforcing materials for polymer-based nanocomposites. Van der Waals interactions between the nanotubes often result in formation of nanotube bundles and/or ropes. Determination of mechanical properties of the nanobundle- and nanorope-based nanocomposites is difficult due to the complicated geometries of the reinforcement structures. However, in order to better utilize nanocomposites, it is crucial to determine mechanical properties of nanocomposites in their real form as much as possible. In this paper, the elasticity theory for anisotropic body and continuum modeling are used to determine effective mechanical properties of bundle and nanorope-based nanocomposites. Numerical models are developed using a Representative Volume Element (RVE) consisting of nanoropes and nanobundles made up of different numbers of nanotubes to investigate the effect of nanorope geometry on nanocomposite mechanical properties. Models of several RVEs are developed with nanoropes consisting of five, seven, nine, and thirteen CNTs. CNT volume fraction is kept constant in all models for a valid comparison. Also, the effect of matrix modulus on the strengthening efficiency of CNTs is investigated. The results indicate that nanocomposite longitudinal modulus decreases with increasing the number of CNTs in the nanorope.