ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE
Several possible definiions of strains in a general shell theory of I.N. Vekua – A.A. Amosov type are considered. The higher-order shell model is definedon a two-dimensional manifold within a set of fieldvariables of the firstkind determined by the expansion factors of the spatial vector fieldof the...
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| Format: | Article |
| Language: | English |
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Publishing House ASV
2021-03-01
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| Series: | International Journal for Computational Civil and Structural Engineering |
| Subjects: | |
| Online Access: | https://ijccse.iasv.ru/index.php/ijccse/article/view/349 |
| _version_ | 1818774557782179840 |
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| author | Sergey Zhavoronok |
| author_facet | Sergey Zhavoronok |
| author_sort | Sergey Zhavoronok |
| collection | DOAJ |
| description | Several possible definiions of strains in a general shell theory of I.N. Vekua – A.A. Amosov type are considered. The higher-order shell model is definedon a two-dimensional manifold within a set of fieldvariables of the firstkind determined by the expansion factors of the spatial vector fieldof the translation. Two base vector systems are introduced, the firs one so-called concomitant corresponds to the cotangent fibrtion of the modelling surface while the other is defind on a surface equidistant to the modelling one. The distortion appears as a two-point tensor referred to both base systems after covariant differentiationof the translation vector feld. Thus, two main definition of the strain tensor become possible, the firstone referred to the main basis whereas the second to the concomitant one. Some possible simplificationsof these tensors are considered, and the interrelation between the general theory of A.A. Amosov type and the classical ones is shown. |
| first_indexed | 2024-12-18T10:43:03Z |
| format | Article |
| id | doaj.art-dc21f4a405594192b26f60fd0dfd510b |
| institution | Directory Open Access Journal |
| issn | 2587-9618 2588-0195 |
| language | English |
| last_indexed | 2024-12-18T10:43:03Z |
| publishDate | 2021-03-01 |
| publisher | Publishing House ASV |
| record_format | Article |
| series | International Journal for Computational Civil and Structural Engineering |
| spelling | doaj.art-dc21f4a405594192b26f60fd0dfd510b2022-12-21T21:10:35ZengPublishing House ASVInternational Journal for Computational Civil and Structural Engineering2587-96182588-01952021-03-0117110.22337/2587-9618-2021-17-1-117-126ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPESergey Zhavoronok0Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, RUSSIASeveral possible definiions of strains in a general shell theory of I.N. Vekua – A.A. Amosov type are considered. The higher-order shell model is definedon a two-dimensional manifold within a set of fieldvariables of the firstkind determined by the expansion factors of the spatial vector fieldof the translation. Two base vector systems are introduced, the firs one so-called concomitant corresponds to the cotangent fibrtion of the modelling surface while the other is defind on a surface equidistant to the modelling one. The distortion appears as a two-point tensor referred to both base systems after covariant differentiationof the translation vector feld. Thus, two main definition of the strain tensor become possible, the firstone referred to the main basis whereas the second to the concomitant one. Some possible simplificationsof these tensors are considered, and the interrelation between the general theory of A.A. Amosov type and the classical ones is shown.https://ijccse.iasv.ru/index.php/ijccse/article/view/349hierarchical modeling of shells, dimensional reduction, analytical continuum dynamics, strain tensors, stress tensors |
| spellingShingle | Sergey Zhavoronok ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE International Journal for Computational Civil and Structural Engineering hierarchical modeling of shells, dimensional reduction, analytical continuum dynamics, strain tensors, stress tensors |
| title | ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE |
| title_full | ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE |
| title_fullStr | ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE |
| title_full_unstemmed | ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE |
| title_short | ON DIFFERENT DEFINITIONS OF STRAIN TENSORS IN GENERAL SHELL THEORIES OF VEKUA-AMOSOV TYPE |
| title_sort | on different definitions of strain tensors in general shell theories of vekua amosov type |
| topic | hierarchical modeling of shells, dimensional reduction, analytical continuum dynamics, strain tensors, stress tensors |
| url | https://ijccse.iasv.ru/index.php/ijccse/article/view/349 |
| work_keys_str_mv | AT sergeyzhavoronok ondifferentdefinitionsofstraintensorsingeneralshelltheoriesofvekuaamosovtype |