The New Approach to Analysis of Thin Isotropic Symmetrical Plates
A new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewri...
| الحاوية / القاعدة: | Applied Sciences |
|---|---|
| المؤلفون الرئيسيون: | , |
| التنسيق: | مقال |
| اللغة: | الإنجليزية |
| منشور في: |
MDPI AG
2020-08-01
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://www.mdpi.com/2076-3417/10/17/5931 |
| _version_ | 1851899431021969408 |
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| author | Mykhaylo Delyavskyy Krystian Rosiński |
| author_facet | Mykhaylo Delyavskyy Krystian Rosiński |
| author_sort | Mykhaylo Delyavskyy |
| collection | DOAJ |
| container_title | Applied Sciences |
| description | A new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewritten as wrapper functions of two arguments. Partial derivatives are calculated using automatic differentiation. A solution of a system of linear equations is substituted to these functions and evaluated using the Einstein summation convention. The calculated results are presented and compared to other analytical and numerical ones. The boundary conditions are satisfied with high accuracy. The effectiveness of the present method is illustrated by examples of rectangular plates. The model can be extended with the ability to solve plates of any shape. |
| format | Article |
| id | doaj-art-30817eebeb3d4c0b9abb4e649e59bbb4 |
| institution | Directory of Open Access Journals |
| issn | 2076-3417 |
| language | English |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-30817eebeb3d4c0b9abb4e649e59bbb42025-08-19T22:06:40ZengMDPI AGApplied Sciences2076-34172020-08-011017593110.3390/app10175931The New Approach to Analysis of Thin Isotropic Symmetrical PlatesMykhaylo Delyavskyy0Krystian Rosiński1Department of Mechanics Construction and Buildings Materials, Faculty of Civil, Architecture and Environmental Engineering, UTP University of Science and Technology, Al. prof. S. Kaliskiego 7, 85-796 Bydgoszcz, PolandDepartment of Mechanics Construction and Buildings Materials, Faculty of Civil, Architecture and Environmental Engineering, UTP University of Science and Technology, Al. prof. S. Kaliskiego 7, 85-796 Bydgoszcz, PolandA new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewritten as wrapper functions of two arguments. Partial derivatives are calculated using automatic differentiation. A solution of a system of linear equations is substituted to these functions and evaluated using the Einstein summation convention. The calculated results are presented and compared to other analytical and numerical ones. The boundary conditions are satisfied with high accuracy. The effectiveness of the present method is illustrated by examples of rectangular plates. The model can be extended with the ability to solve plates of any shape.https://www.mdpi.com/2076-3417/10/17/5931mathematical modelplate analysisisotropic symmetrical plateautomatic differentiation |
| spellingShingle | Mykhaylo Delyavskyy Krystian Rosiński The New Approach to Analysis of Thin Isotropic Symmetrical Plates mathematical model plate analysis isotropic symmetrical plate automatic differentiation |
| title | The New Approach to Analysis of Thin Isotropic Symmetrical Plates |
| title_full | The New Approach to Analysis of Thin Isotropic Symmetrical Plates |
| title_fullStr | The New Approach to Analysis of Thin Isotropic Symmetrical Plates |
| title_full_unstemmed | The New Approach to Analysis of Thin Isotropic Symmetrical Plates |
| title_short | The New Approach to Analysis of Thin Isotropic Symmetrical Plates |
| title_sort | new approach to analysis of thin isotropic symmetrical plates |
| topic | mathematical model plate analysis isotropic symmetrical plate automatic differentiation |
| url | https://www.mdpi.com/2076-3417/10/17/5931 |
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