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Загальна кількість знайдених документів : 2 Представлено документи з 1 до 2 |
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| 1. | 
Kagadiy T. Mathematical modeling in the calculation of reinforcing elements [Електронний ресурс] / T. Kagadiy, A. Shporta // Науковий вісник Національного гірничого університету. - 2019. - № 5. - С. 60-64. - Режим доступу: http://nbuv.gov.ua/UJRN/Nvngu_2019_5_12 Purpose. Determination of stress distribution laws for the hard stamp and an elastic plate interaction with cylindrical anisotropy. Simulation of contact interaction tasks in order to determine the processes of wear, strength, destruction and structures durability. Development of analytical methods for calculating contact interactions of structures taking into account various material properties. Methodology. The mathematical model spatial problem of a hard stamp and a circular sector with cylindrical anisotropy interaction has been compiled. To study the model, an asymptotic method has been proposed, which allows dividing the stress-strain state of an infinite circular sector into two components and reducing the solution of the elasticity theory problem to the sequential solution of potential theory problems. Findings. A concrete contact problem was investigated, for which the asymptotic method was used. The solution takes into account the friction that occurs in the interaction process between the rigid stamp and the elastic plate. The considered task is new and rather difficult. It causes significant difficulties when considered. Therefore, the obtained analytical solution is a useful result for further analysis or numerical calculations. The pressure values under the stamp were found, the influence of friction was taken into account. Originality. The previously proposed method is generalized to the case of material cylindrical anisotropy. An analytical solution has been obtained for a new complex spatial contact problem. Practical value. The asymptotic method proposed in the paper allows us to move from mechanics solving complex mixed problems to solving sequential boundary problems of potential theory - the most developed section of mathematical physics. The solutions obtained by the proposed method make it possible to analyze the stress-strain state that occurs when a hard stamp is pressed into the free face of an elastic orthotropic infinite circular sector with cylindrical anisotropy, the edges of which are fixed. The following problem is considered: in the free edge of an infinite circular sector, which is elastic, orthotropic, and also its material possesses the properties of cylindrical anisotropy, a rigid stamp is pressed. The edges of the circular sector are fixed. Application of the obtained results is possible at the calculation and design of various types of fastenings. The results can be used in calculating and designing various types of mounts. | ||
| 2. |
Shporta A. Asymptotic method in two-dimensional problems of electroelasticity [Електронний ресурс] / A. Shporta, T. Kagadiy, O. Onopriienko // Науковий вісник Національного гірничого університету. - 2020. - № 1. - С. 130-134. - Режим доступу: http://nbuv.gov.ua/UJRN/Nvngu_2020_1_24 Purpose. Generalization of the asymptotic method for solving two-dimensional problems of electroelasticity. Accounting for electric charges arising from deformation on the surfaces of piezoelectric materials. Checking the possibility of taking into account the magnetic field and the opposite effect when exposed to an electric field. Methodology. The mathematical model of the piezoelectric material is described using the equilibrium equations, the electroelastic state, and the Cauchy relations. A small parameter is introduced as a ratio of the physical characteristics of the material. Transformations of coordinates and desired functions depending on the specified parameter are proposed. Findings. The introduction of these transformations allowed splitting the initial boundary-value problem into two components with different properties. Each of them contains both mechanical and electrical components. The solution is sought as a superposition of solutions of both types. Each of the types of stress-strain states contains the main function and an auxiliary one. The expansion of the desired functions in rows by parameter e and the construction of asymptotic sequences lead to the fact that in each approximation the main functions are sought from the Laplace or Poisson equations. Auxiliary ones are found by integration. The analysis of the boundary conditions is given. It is shown that they can almost always be formulated for basic functions. Originality. The method proposed earlier by the authors for reducing the boundary value problems of linear and nonlinear elasticity theory to the sequential solution of potential theory problems is generalized for the case of modern piezoelectric materials described by electroelasticity equations. Practical value. With the help of the proposed approach, analytical solutions of practically important problems of electroelasticity can be obtained; estimates of the stress-strain state of products from piezoelectric materials are carried out. The results can be used as null approximations in numerical calculations. | ||
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