A crack with partially loaded faces between two piezoelectric materials

Розглянуто тріщину між двома п’єзоелектричними півплощинами, береги якої завантажені нормальними та дотичними напруженнями, що забезпечують розкриття тріщини. Вважається, що ці напруження рівномірно розподілені по відрізках, що примикають до вершин тріщини. Використовуючи представлення шуканих факторів через комплексні потенціали, проблема зведена до задачі лінійного спряження, розв’язок якої представлений у вигляді інтегралів типу Коші. Основна увага приділена знаходженню нормального та дотичного стрибків переміщень. Отримано замкнені представлення цих факторів через гіпергеометричні функції. Крім того, використовуючи малість біматеріального параметра, отримано наближені асимптотичні формули. На конкретних прикладах шляхом порівняння результатів розрахунків показано, що вказані наближені формули для стрибків переміщень мають високу точність як для п’єзоелектричних, так і для ізотропних матеріалів.A crack between two piezoelectric half-plane loaded by normal and shear stresses is considered. It is assumed that the stresses are uniformly distributed over the segments adjacent to the crack tips. Using the representation of the unknown factors through the complex potentials, the problem is reduced to the problem of linear relationship with respect to the function analytic in the whole plane except the crack region. The solution of this problem is presented in the form of Cauchy type integrals and the stresses and the derivatives of the displacement jumps are presented in the form of such integrals. Further, the main attention is paid to the determination of the normal and tangent jumps of displacements over the crack region. Applying the Sokhotski–Plemelj theorem and performing the integration the closed presentation of these factors through the hypergeometric functions are obtained. These formulas are complicated and in many cases they are inconvenient for numerical analysis. However the obtained solution depends on the bimaterial parameter, which is very small for most of piezoelectric material combinations. Therefore in addition, the approximate asymptotic formula is obtained using the smallness of the mentioned parameter. Similar analysis has been performed for a crack between two isotropic materials as well and exact and approximate formulas for the normal and shear displacement jumps and their derivatives are presented in this case as well. The numerical analysis has been performed for the typical piezoelectric materials PZT-4 and PZT-5 and the normal and shear crack openings calculated by exact and approximate formulas are presented graphically. Similar figures for a crack in the isotropic bimaterial are presented as well. In all considered cases the comparing of the calculation results show that the approximate formulas for jumps of displacements have high accuracy for both piezoelectric and for isotropic materials. It means that that these approximate formulas can be used for the analysis of interface cracks with pre-fracture zones

Computer simulation of functioning of elements of security systems

The article is devoted to issues of development of the informational complex for simulation of functioning of the security system elements. The complex is described from the point of view of main objectives, a design concept and an interrelation of main elements. The proposed conception of the computer simulation provides an opportunity to simulate processes of security system work for training security staff during normal and emergency operation

On the Issue of Labor Relations Discontinuance by Staff Reduction

This article is devoted to consideration of issues related to the procedure of labor law contract termination by staff reduction. The author, analyzing the judicial practice, gives practical recommendations on the procedure of employment relationships discontinuance

Simulation of the effectiveness evaluation process of security systems

The paper is devoted to issues of creation of cross-functional analytical complex for simulation of the process of operation of the security system elements. Basic objectives, a design concept and an interrelation of main elements of the complex are described. The proposed conception of the analytical complex provides an opportunity to simulate processes for evaluating the effectiveness of physical protection system of a nuclear facility. The complex uses models, that take into account features of the object, parameters of technical means and tactics of adversaries. Recommendations were made for applying of this conception for training specialists in the field of physical protection of nuclear materials

Issues of conservative treatment of patients with flatfoot

Flatfoot is the most common foot disease, the prevalence of which is 30-70% according to many authors. Planovalgus foot deformity asymptomatically existing for a long time can further lead to pain syndrome and limping, sensitivity disorders, trophic disorders, limitation of foot joints mobility, development of arthritic changes with corresponding progression of the function impairment. Timely initiation of treatment, complex pathogenetic and symptomatic therapy as well as strict adherence to the doctor's recommendations help to achieve maximum effect. The aims of treatment of patients with flatfoot are posture stabilization and support of overloaded zones of the plantar surface, improvement of supply of the foot and musculoskeletal apparatus, as well as foot joints, and reduction of pain syndrome. Despite the prevalence of pathology, as well as a wide range of methods of treatment and rehabilitation, conservative treatment does not always lead to a positive result and the problem remains unresolved. This literature review describes the main directions of conservative therapy of patients with flatfoot from the view of evidence-based medicine. The data on the use of special ortheses and orthopedic shoes for correcting the foot deformities are discussed with a description of possible complications. The main forms of exercise therapy used to stabilize the foot muscles tonus, are analyzed. The application of physiotherapeutic factors aimed at improving trophic and blood supply of tissues, as well as strengthening of the musculoskeletal apparatus of the lower legs and feet, is described. Data on the use of complex conservative treatment of patients with flatfoot are presented. The article also focuses on the use of drug therapy as part of the complex treatment

Efficiency of use of packages of applied programs at studying mathematical disciplines

Предложена концепция системного использования ИНТ в преподавании большинства дисциплин в техническом университете. Ее реализация на примере курса высшей математики привела к разработке и внедрению инновационной образовательной технологии преподавания дисциплин математического и естественнонаучного циклов.The concept of system use IT in teaching the majority of disciplines in a technical univercity is offered. Its realization by the example of higher mathematics has resulted in development and introduction of innovational educational technology of teaching of disciplines of a mathematical and natural-science cycle

SOCIAL INTERACTION OF LARGE BUSINESSES AS A SECURITY CONDITION OF ITS OPERATION AND DEVELOPMENT IN THE NORTHERN REGION

Purpose: The aim of the research is to identify social interaction of large businesses as a security condition of its operation and development in the northern region. Methodology: This is descriptive-analytic research whose data are obtained through library studies and analytical resources. Data analysis is based on content analysis and analytical comparison. Result: Results showed that to improve the safety of large businesses in the Northern region continuous socially-oriented activities aimed at improving the quality of life of the population of the region of presence with the support of various social initiatives in the region of presence are required. Applications: This research can be used for businessmen and developers. Novelty/Originality: In this research, the model of social interaction of large businesses is presented in a comprehensive and complete manner

Thermonuclear energy is a future source of energy

With the development of nuclear physics, the problem of getting energy from nuclear fusion is topical nowadays. Despite all the difficulties in implementation, thermonuclear energy is a highly efficient source. Therefore, this kind of energy can become a base of economical potential of the country