Mathematical modeling of contact interaction of two electroelastic half-spaces (without electrode coating of surfaces) in the presence of a hard disk-like inclusion between them and pressure in the area of separation

Based on the use of a rigorous mathematical model that takes into account the connectivity of force and electric fields in electroelastic bodies, the contact interaction of two piezoelectric transversely isotropic half-spaces with different properties under compression (in the presence of a hard disk-shaped inclusion between them and pressure in the material separation region) was studied. The solution to the problem is obtained by representing the general solution of the static equations of the electroelasticity for a transversely isotropic body in terms of harmonic functions, followed by the construction of the boundary value problem of the electroelasticity to the consideration of the integral equation and the expansion of the desired function in a small parameter. As a special case from the constructed analytical expressions, the main parameters of the contact for two elastic transversely isotropic and isotropic half-spaces (with the inclusion between them and pressure in the separation region) are implied. Numerical results were obtained. The influence was studied of the electroelastic properties of half-spaces, the geometric dimensions of the inclusion, and loads on the parameters of the contact interaction of electroelastic bodies.

Simulation of nonstationary hydrogen diffusion processes near the crack tip in a field of inhomogeneous mechanical stresses

An elastic-plastic isotropic body is investigated, weakened by a rectilinear crack directed along the abscissa axis, under the action of stresses symmetric with respect to its plane. The hydrogen concentration near the crack tip is calculated. An approximate solution of this problem is constructed under the condition that the distribution of hydrostatic stresses along the crack extension is approximated by a parabola. For a numerical solution, a method of the third order of accuracy with a two-sided estimate of the main term of the local error is proposed.

Fractal characteristics of geomorphological heterogeneity in Xisha Islands waters under Multiple Linear Regression

Based on the obvious anisotropy of Xisha Islands waters topography, the uneven fractal characteristics of Xisha Islands waters topography are studied by using multivariate linear expression. Using multiple linear regression analysis method to extract the projection of heterogeneous characteristic factors, the geometric heterogeneous characteristics of Xisha Islands waters are obtained. The fractal feature of landform is studied based on projection coverage method, and the non-isotropic body irregularity in Xisha Islands waters is measured. Experimental results show that this method can effectively analyze the non-uniform fractal characteristics of the Xisha Islands waters. The fractal dimension of different types of landforms in Xisha Islands in the corresponding region is high mountain area > medium and low mountain area > basin area, which reflects the difference of surface roughness or complexity of different types of landforms. The calculated fractal dimension is helpful to reveal the heterogeneity of general geomorphological features in different development stages.

Stress–temperature equations of motion of Ignaczak and Beltrami–Michell types in arbitrary curve coordinate system: معادلات الحركة بلغة الإجهادات والحرارة من نوعي إغناتشاك وبيلترامي– ميشيل في أي نظام احداثي منحني

This paper relates to the mathematical linear model of the elastic, homogeneous and isotropic body, with neglected structure and infinitesimal elastic strains, subjected to temperature field; discussed by Hooke, and shortly called (H). We firstly introduce the variable tensorial forms of the traditional and Lame descriptions of the coupled dynamic state of considerable Hooke body, in an arbitrary curve coordinate system. We study the variable tensorial forms in an arbitrary curve coordinate system, of the generalized Beltrami–Michell stress-temperature equations, and of the stress-temperature Ignaczak equations and its completeness problem for the (H) thermoelastic body.

The Generalized Thermodynamical Beltrami – Michell Tensorial Equations for the general Thermodynamical State of the Hooke Body: معادلات بيلترامي- ميشيل التنسورية الترموديناميكية المعممة لأجل الحالة الترموديناميكية العامة لجسم هوك

This paper concerns the mathematical linear model of the elastic, homogeneous and isotropic body, with no considerable structure and with infinitesimal elastic strains, subjected to Thermal effects, in the frame of coupled thermoelectrodynamics; discussed firstly by Hooke (in the isothermal case), and shortly called (H). In this paper, firstly we introduce the invariable tensorial traditional and Lame descriptions of the coupled dynamic, thermoelastic, homogeneous and isotropic Hooke body, which initial configuration forms a simply-connected region in the three dimensional euclidean manifold. The news of this paper consists in deriving the invariable tensorial, generalized Beltrami – Michell stress-temperature equations for the (H) thermoelastic body (in the more general case than the thermal stress state), which initial configuration forms a simply-connected region in the three dimensional euclidean manifold. Finally, we end the paper by suggesting the problem for discussing, in addition to another open problem.

Fine elastic circular inclusion in the area of harmonic vibrations of an unlimited body under smooth contact

Fine elastic circular inclusion in the area of harmonic vibrations of an unlimited body under smooth contact The problem of the interaction of harmonic waves with a thin elastic circular inclusion, which is located in an elastic isotropic body (matrix), is solved. On both sides of the inclusion between it and the body (matrix), the conditions of smooth contact are realized. The solution method is based on representing the displacements in the matrix through discontinuous solutions of the Lamé equations for harmonic vibrations. This made it possible to reduce the problem to Fredholm integral equations of the second kind with respect to functions associated with jumps in normal stress and radial displacement to included ones. After the realization of the boundary conditions on the sides of the inclusion, a system of singular integral equations is obtained to determine these jumps. Keywords: elastic inclusions, cylindrical waves, matrix, stress intensity factor.