Nonlinear differential equations with moving singular points require emergence and development of new approximate methods of solution. In this paper, we give a solution to one of the problems of the analytical approximate method for solving nonlinear differential equations with moving singular points, and study the influence of the perturbation of the initial conditions on the analytical approximate solution in the analytic domain. Theoretical material was tested using a numerical experiment confirming its reliability. The theoretical material presented in this paper allows researchers to use nonlinear differential equations with moving singular points when designing mathematical models of building structures.
Currently, wind energy is one of the most developing areas, which is primarily due to the absence of emissions of harmful substances into the atmosphere. Wind power allows providing electricity to remote areas, where fuel delivery, as well as the construction of thermal power plants is laborious and expensive. The effective development of wind turbines should solve the following tasks: the creation of the necessary driving force and the possibility of using a high coefficient of wind energy, which does not contradict the maintenance of the ecological balance of the territory. An electric generator for a household wind turbine must provide electricity in a wide range of rotation speeds and be able to work independently without automation and external energy sources. The study of the numerical implementation of the method of aerodynamic analysis of the wind turbine blade in rotational motion in the ANSYS CFD software package is by far the most promising and dynamically developing direction in the field of aerodynamics calculations. The results of approbation of the mixed calculation method using a dynamically variable and stationary finite-volume mesh are presented. The use of a mixed design scheme allows for calculations of wind turbines inside the building, while it becomes possible to minimize the required power for the study.
For a number of materials used in modern practice, calculations according to the classical theory of elasticity give incorrect results. To ensure the reliable operation of structures, there is a need for new theories. At present, of particular interest for practical applications is the asymmetric moment theory of elasticity. In the work, by the method of hypotheses, the three-dimensional equations of the moment asymmetric theory of elasticity are reduced to the equations of the theory of plates. The hypotheses of the theory of plates in the moment theory of elasticity are formulated on the basis of previously obtained our results of the reduction of three-dimensional equations to two-dimensional theories by a mathematical method. Just as in the classical theory of elasticity, the complete problem of the moment theory of plates is divided into two problems - a plane problem and a problem of plate bending. The equations of the plane problem have been obtained in many papers. The situation is different with the construction of the theory of plate bending in the moment theory of elasticity. In this work, for the first time, substantiated hypotheses are formulated and a consistent theory of plate bending is presented. A numerical calculation of the bending of a rectangular hinged plate is carried out according to the obtained applied theory. The calculation results are presented in the form of graphs.
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