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.

Solution of tasks for elastoplastic transversal isotropic bodies

In this article: the theorem has been proven for existence and uniqueness of the generalized solution of elastoplastic boundary problem based on the theory of plastic yielding of transversal isotropic bodies from the loading surface in the deformation and stress space.

The Implementation of Algorithm Iterative Conversion for Three-Component Composite on the Example of Solution of the Bending Plate Problem

Applications of the new algorithm for the calculation of stress-strain state of multicomponent isotropic bodies are given in the article. The algorithm is based on the derivation of expressions for iterated effective modules obtained by converting the Voigt-Reuss modules. The comparison of exact solution with the solutions based on new characteristics obtained for the problem of loading a round sandwich plate is given as the example.

Explicit Solutions of the Boundary Value Problems for an Ellipse with Double Porosity

The basic two-dimensional boundary value problems of the fully coupled linear equilibrium theory of elasticity for solids with double porosity structure are reduced to the solvability of two types of a problem. The first one is the BVPs for the equations of classical elasticity of isotropic bodies, and the other is the BVPs for the equations of pore and fissure fluid pressures. The solutions of these equations are presented by means of elementary (harmonic, metaharmonic, and biharmonic) functions. On the basis of the gained results, we constructed an explicit solution of some basic BVPs for an ellipse in the form of absolutely uniformly convergent series.