The New Approach to Analysis of Thin Isotropic Symmetrical Plates

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...

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Main Authors: Mykhaylo Delyavskyy, Krystian Rosiński
Format: Article
Language:English
Published: MDPI AG 2020-08-01
Series:Applied Sciences
Subjects:
mathematical model
plate analysis
isotropic symmetrical plate
automatic differentiation
Online Access:https://www.mdpi.com/2076-3417/10/17/5931
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spelling doaj-30817eebeb3d4c0b9abb4e649e59bbb42020-11-25T03:49:56ZengMDPI AGApplied Sciences2076-34172020-08-01105931593110.3390/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
collection DOAJ
language English
format Article
sources DOAJ
author Mykhaylo Delyavskyy
Krystian Rosiński
spellingShingle Mykhaylo Delyavskyy
Krystian Rosiński
The New Approach to Analysis of Thin Isotropic Symmetrical Plates
Applied Sciences
mathematical model
plate analysis
isotropic symmetrical plate
automatic differentiation
author_facet Mykhaylo Delyavskyy
Krystian Rosiński
author_sort Mykhaylo Delyavskyy
title The New Approach to Analysis of Thin Isotropic Symmetrical Plates
title_short 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_sort new approach to analysis of thin isotropic symmetrical plates
publisher MDPI AG
series Applied Sciences
issn 2076-3417
publishDate 2020-08-01
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.
topic mathematical model
plate analysis
isotropic symmetrical plate
automatic differentiation
url https://www.mdpi.com/2076-3417/10/17/5931
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AT krystianrosinski newapproachtoanalysisofthinisotropicsymmetricalplates
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