Mathematical modeling of the process of nonlinear deformation of thin-walled structures
Objective. The objective is to develop a unified method for solving a general nonlinear boundary value problem associated with discontinuous phenomena, which allows identifying all the characteristic features of the behavior of thin-walled systems under load. The issues of nonlinear deformation, los...
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| Format: | Article |
| Language: | Russian |
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Dagestan State Technical University
2025-01-01
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| Series: | Вестник Дагестанского государственного технического университета: Технические науки |
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| Online Access: | https://vestnik.dgtu.ru/jour/article/view/1633 |
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| _version_ | 1849410153098510336 |
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| author | G. M. Murtazaliev M. M. Paizulaev |
| author_facet | G. M. Murtazaliev M. M. Paizulaev |
| author_sort | G. M. Murtazaliev |
| collection | DOAJ |
| description | Objective. The objective is to develop a unified method for solving a general nonlinear boundary value problem associated with discontinuous phenomena, which allows identifying all the characteristic features of the behavior of thin-walled systems under load. The issues of nonlinear deformation, loss of stability of the initial equilibrium shape and post-critical behavior are considered using the example of a thin spherical shell. Method. The problem is solved by numerical and analytical methods, representing a set of methods of catastrophe theory and the finite difference method of increased accuracy. The main attention is paid to the mathematical aspects of the phenomena under consideration. Result. The parameters of the stressstrain state of subcritical, critical and postcritical deformation are determined using a spherical shell as an example. The relationships between the limit and bifurcation values of the load parameters are obtained, allowing us to determine the group of the limit state of the achieved level of the stress-strain state of the structure. Conclusion. The solution of the general problem allows us to obtain complete and necessary information to determine the degree of danger of the states of structures and ensure their reliability. |
| format | Article |
| id | doaj-art-9a4172e5ba9047b581e1e5437c135dbe |
| institution | Kabale University |
| issn | 2073-6185 2542-095X |
| language | Russian |
| publishDate | 2025-01-01 |
| publisher | Dagestan State Technical University |
| record_format | Article |
| series | Вестник Дагестанского государственного технического университета: Технические науки |
| spelling | doaj-art-9a4172e5ba9047b581e1e5437c135dbe2025-08-20T03:35:14ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2025-01-0151420921610.21822/2073-6185-2024-51-4-209-216946Mathematical modeling of the process of nonlinear deformation of thin-walled structuresG. M. Murtazaliev0M. M. Paizulaev1Daghestan State Technical UniversityDaghestan State Technical UniversityObjective. The objective is to develop a unified method for solving a general nonlinear boundary value problem associated with discontinuous phenomena, which allows identifying all the characteristic features of the behavior of thin-walled systems under load. The issues of nonlinear deformation, loss of stability of the initial equilibrium shape and post-critical behavior are considered using the example of a thin spherical shell. Method. The problem is solved by numerical and analytical methods, representing a set of methods of catastrophe theory and the finite difference method of increased accuracy. The main attention is paid to the mathematical aspects of the phenomena under consideration. Result. The parameters of the stressstrain state of subcritical, critical and postcritical deformation are determined using a spherical shell as an example. The relationships between the limit and bifurcation values of the load parameters are obtained, allowing us to determine the group of the limit state of the achieved level of the stress-strain state of the structure. Conclusion. The solution of the general problem allows us to obtain complete and necessary information to determine the degree of danger of the states of structures and ensure their reliability.https://vestnik.dgtu.ru/jour/article/view/1633nonlinear problemssingular pointsdiscontinuous phenomenacatastrophe theoryloss of stabilitypost-critical behavior |
| spellingShingle | G. M. Murtazaliev M. M. Paizulaev Mathematical modeling of the process of nonlinear deformation of thin-walled structures Вестник Дагестанского государственного технического университета: Технические науки nonlinear problems singular points discontinuous phenomena catastrophe theory loss of stability post-critical behavior |
| title | Mathematical modeling of the process of nonlinear deformation of thin-walled structures |
| title_full | Mathematical modeling of the process of nonlinear deformation of thin-walled structures |
| title_fullStr | Mathematical modeling of the process of nonlinear deformation of thin-walled structures |
| title_full_unstemmed | Mathematical modeling of the process of nonlinear deformation of thin-walled structures |
| title_short | Mathematical modeling of the process of nonlinear deformation of thin-walled structures |
| title_sort | mathematical modeling of the process of nonlinear deformation of thin walled structures |
| topic | nonlinear problems singular points discontinuous phenomena catastrophe theory loss of stability post-critical behavior |
| url | https://vestnik.dgtu.ru/jour/article/view/1633 |
| work_keys_str_mv | AT gmmurtazaliev mathematicalmodelingoftheprocessofnonlineardeformationofthinwalledstructures AT mmpaizulaev mathematicalmodelingoftheprocessofnonlineardeformationofthinwalledstructures |