Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports
The main goal of deformable solid mechanics is to determine the stress–strain state of parts, structural elements, and their connections. The most accurate results of calculations of this state allow us to optimize design objects. However, not all models can be solved using exact methods. One such m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/11/9/172 |
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| author | Vitaly Miroshnikov Oleksandr Savin Vladimir Sobol Vyacheslav Nikichanov |
| author_facet | Vitaly Miroshnikov Oleksandr Savin Vladimir Sobol Vyacheslav Nikichanov |
| author_sort | Vitaly Miroshnikov |
| collection | DOAJ |
| description | The main goal of deformable solid mechanics is to determine the stress–strain state of parts, structural elements, and their connections. The most accurate results of calculations of this state allow us to optimize design objects. However, not all models can be solved using exact methods. One such model is the problem of a layer with cylindrical embedded supports that are parallel to each other and the layer boundaries. In this work, the supports are represented by cylindrical cavities with zero displacements set on them. The layer is considered in Cartesian coordinates, and the cavities are in cylindrical coordinates. To solve the problem, the Lamé equation is used, where the basic solutions between different coordinate systems are linked using the generalized Fourier method. By satisfying the boundary conditions and linking different coordinate systems, a system of infinite linear algebraic equations is created. For numerical realization, the method of reduction is used to find the unknowns. The numerical analysis has shown that the boundary conditions are fulfilled with high accuracy, and the physical pattern of the stress distribution and the comparison with results of similar studies indicate the accuracy of the obtained results. The proposed method for calculating the stress–strain state can be applied to the calculation of structures whose model is a layer with cylindrical embedded supports. The numerical results of the work make it possible to predetermine the geometric parameters of the model to be designed. |
| first_indexed | 2024-03-10T22:53:49Z |
| format | Article |
| id | doaj.art-0a0ce2fb35234a2a9c686b6d3cb1a90c |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-10T22:53:49Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-0a0ce2fb35234a2a9c686b6d3cb1a90c2023-11-19T10:07:05ZengMDPI AGComputation2079-31972023-09-0111917210.3390/computation11090172Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded SupportsVitaly Miroshnikov0Oleksandr Savin1Vladimir Sobol2Vyacheslav Nikichanov3Department of Aircraft Strength, National Aerospace University “KHAI”, 61000 Kharkiv, UkraineDepartment of Aircraft Strength, National Aerospace University “KHAI”, 61000 Kharkiv, UkraineDepartment of Aircraft Strength, National Aerospace University “KHAI”, 61000 Kharkiv, UkraineDepartment of Aircraft Production Technology, National Aerospace University “KHAI”, 61000 Kharkiv, UkraineThe main goal of deformable solid mechanics is to determine the stress–strain state of parts, structural elements, and their connections. The most accurate results of calculations of this state allow us to optimize design objects. However, not all models can be solved using exact methods. One such model is the problem of a layer with cylindrical embedded supports that are parallel to each other and the layer boundaries. In this work, the supports are represented by cylindrical cavities with zero displacements set on them. The layer is considered in Cartesian coordinates, and the cavities are in cylindrical coordinates. To solve the problem, the Lamé equation is used, where the basic solutions between different coordinate systems are linked using the generalized Fourier method. By satisfying the boundary conditions and linking different coordinate systems, a system of infinite linear algebraic equations is created. For numerical realization, the method of reduction is used to find the unknowns. The numerical analysis has shown that the boundary conditions are fulfilled with high accuracy, and the physical pattern of the stress distribution and the comparison with results of similar studies indicate the accuracy of the obtained results. The proposed method for calculating the stress–strain state can be applied to the calculation of structures whose model is a layer with cylindrical embedded supports. The numerical results of the work make it possible to predetermine the geometric parameters of the model to be designed.https://www.mdpi.com/2079-3197/11/9/172Lamé equationembedded supportscylindrical cavity in a layergeneralized Fourier method |
| spellingShingle | Vitaly Miroshnikov Oleksandr Savin Vladimir Sobol Vyacheslav Nikichanov Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports Computation Lamé equation embedded supports cylindrical cavity in a layer generalized Fourier method |
| title | Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports |
| title_full | Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports |
| title_fullStr | Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports |
| title_full_unstemmed | Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports |
| title_short | Solving the Problem of Elasticity for a Layer with N Cylindrical Embedded Supports |
| title_sort | solving the problem of elasticity for a layer with n cylindrical embedded supports |
| topic | Lamé equation embedded supports cylindrical cavity in a layer generalized Fourier method |
| url | https://www.mdpi.com/2079-3197/11/9/172 |
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