Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting
The study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under cons...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2020-06-01
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| Series: | Curved and Layered Structures |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/cls-2020-0005 |
| _version_ | 1818390515812401152 |
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| author | Duissenbekov Bolat Tokmuratov Abduhalyk Zhangabay Nurlan Orazbayev Zhenis Yerimbetov Baisbay Aldiyarov Zhumadilla |
| author_facet | Duissenbekov Bolat Tokmuratov Abduhalyk Zhangabay Nurlan Orazbayev Zhenis Yerimbetov Baisbay Aldiyarov Zhumadilla |
| author_sort | Duissenbekov Bolat |
| collection | DOAJ |
| description | The study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval. |
| first_indexed | 2024-12-14T04:58:52Z |
| format | Article |
| id | doaj.art-726bfa3ad3214e0f9c39bbf5b308ad70 |
| institution | Directory Open Access Journal |
| issn | 2353-7396 |
| language | English |
| last_indexed | 2024-12-14T04:58:52Z |
| publishDate | 2020-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Curved and Layered Structures |
| spelling | doaj.art-726bfa3ad3214e0f9c39bbf5b308ad702022-12-21T23:16:16ZengDe GruyterCurved and Layered Structures2353-73962020-06-0171485510.1515/cls-2020-0005cls-2020-0005Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear settingDuissenbekov Bolat0Tokmuratov Abduhalyk1Zhangabay Nurlan2Orazbayev Zhenis3Yerimbetov Baisbay4Aldiyarov Zhumadilla5M. Auezov South Kazakhstan State University, Tauke Khan Ave 5, Shymkent 160012, KazakhstanM. Auezov South Kazakhstan State University, Tauke Khan Ave 5, Shymkent 160012, KazakhstanM. Auezov South Kazakhstan State University, Tauke Khan Ave 5, Shymkent 160012, KazakhstanM. Auezov South Kazakhstan State University, Tauke Khan Ave 5, Shymkent 160012, KazakhstanM. Auezov South Kazakhstan State University, Tauke Khan Ave 5, Shymkent 160012, KazakhstanM. Auezov South Kazakhstan State University, Tauke Khan Ave 5, Shymkent 160012, KazakhstanThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.https://doi.org/10.1515/cls-2020-0005concrete shelldifferential equationsnonlinear deformationsfinite differenceconcrete creepcauchy problem |
| spellingShingle | Duissenbekov Bolat Tokmuratov Abduhalyk Zhangabay Nurlan Orazbayev Zhenis Yerimbetov Baisbay Aldiyarov Zhumadilla Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting Curved and Layered Structures concrete shell differential equations nonlinear deformations finite difference concrete creep cauchy problem |
| title | Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting |
| title_full | Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting |
| title_fullStr | Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting |
| title_full_unstemmed | Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting |
| title_short | Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting |
| title_sort | finite difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting |
| topic | concrete shell differential equations nonlinear deformations finite difference concrete creep cauchy problem |
| url | https://doi.org/10.1515/cls-2020-0005 |
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