Bending of multilayer beam slabs lying on an elastic half-space
Mathematical models and analytical methods for solving contact problems of multilayer beam slabs lying on an elastic base are developed, considering the reactive normal and shear pressures of the base. In this case, an elastic filler is inserted between each pair of beam slabs. The rigidity of the f...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Peter the Great St. Petersburg Polytechnic University
2024-09-01
|
| Series: | Magazine of Civil Engineering |
| Subjects: | |
| Online Access: | http://engstroy.spbstu.ru/article/2024.130.04/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849722129656840192 |
|---|---|
| author | Mirsaidov Mirziyod Mirsaidovich Vatin Nikolai Ivanovich Mamasoliev Kazokboy |
| author_facet | Mirsaidov Mirziyod Mirsaidovich Vatin Nikolai Ivanovich Mamasoliev Kazokboy |
| author_sort | Mirsaidov Mirziyod Mirsaidovich |
| collection | DOAJ |
| description | Mathematical models and analytical methods for solving contact problems of multilayer beam slabs lying on an elastic base are developed, considering the reactive normal and shear pressures of the base. In this case, an elastic filler is inserted between each pair of beam slabs. The rigidity of the filler placed between the slabs can differ in each layer. Each slab beam is subject to external loads and pressure of the filler. The stiffness coefficients of beam slabs are discrete and variable. The lower beam slab, which has a two-way connection with the elastic base, is under the influence (except for external loads) of reactive normal and shear pressure of the base. The mathematical model of the problem includes closed systems of integro-differential equations with corresponding boundary conditions. To solve the problem, an analytical method based on the approximation of Chebyshev orthogonal polynomials was used. The solution to the problem is reduced to the study of infinite systems of algebraic equations. The regularity of the resulting infinite system of equations is proven. To solve it, the reduction method was used. A test example is considered and a numerical solution to algebraic equations is obtained. The internal force factors arising in the beam slab are also investigated. Based on the analysis of numerical results, some new results were identified, i.e., a significant influence of the filler and the reactive pressure of the base on the internal force factors of the beam slab, etc. |
| format | Article |
| id | doaj-art-748a4d12e8d5407ca745dff70f02700e |
| institution | DOAJ |
| issn | 2712-8172 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Peter the Great St. Petersburg Polytechnic University |
| record_format | Article |
| series | Magazine of Civil Engineering |
| spelling | doaj-art-748a4d12e8d5407ca745dff70f02700e2025-08-20T03:11:26ZengPeter the Great St. Petersburg Polytechnic UniversityMagazine of Civil Engineering2712-81722024-09-01170610.34910/MCE.130.420714726Bending of multilayer beam slabs lying on an elastic half-spaceMirsaidov Mirziyod Mirsaidovich0https://orcid.org/0000-0002-8907-7869Vatin Nikolai Ivanovich1https://orcid.org/0000-0002-1196-8004Mamasoliev Kazokboy2https://orcid.org/0000-0003-3371-5742Tashkent Institute of Irrigation and Agricultural Mechanization EngineersPeter the Great St. Petersburg Polytechnic UniversitySamarkand State Institute of Architecture and Civil EngineeringMathematical models and analytical methods for solving contact problems of multilayer beam slabs lying on an elastic base are developed, considering the reactive normal and shear pressures of the base. In this case, an elastic filler is inserted between each pair of beam slabs. The rigidity of the filler placed between the slabs can differ in each layer. Each slab beam is subject to external loads and pressure of the filler. The stiffness coefficients of beam slabs are discrete and variable. The lower beam slab, which has a two-way connection with the elastic base, is under the influence (except for external loads) of reactive normal and shear pressure of the base. The mathematical model of the problem includes closed systems of integro-differential equations with corresponding boundary conditions. To solve the problem, an analytical method based on the approximation of Chebyshev orthogonal polynomials was used. The solution to the problem is reduced to the study of infinite systems of algebraic equations. The regularity of the resulting infinite system of equations is proven. To solve it, the reduction method was used. A test example is considered and a numerical solution to algebraic equations is obtained. The internal force factors arising in the beam slab are also investigated. Based on the analysis of numerical results, some new results were identified, i.e., a significant influence of the filler and the reactive pressure of the base on the internal force factors of the beam slab, etc.http://engstroy.spbstu.ru/article/2024.130.04/multilayer beam slabinteractionhalf-spaceshear stressfillerrigiditydiscretenesscontact conditionsregularity |
| spellingShingle | Mirsaidov Mirziyod Mirsaidovich Vatin Nikolai Ivanovich Mamasoliev Kazokboy Bending of multilayer beam slabs lying on an elastic half-space Magazine of Civil Engineering multilayer beam slab interaction half-space shear stress filler rigidity discreteness contact conditions regularity |
| title | Bending of multilayer beam slabs lying on an elastic half-space |
| title_full | Bending of multilayer beam slabs lying on an elastic half-space |
| title_fullStr | Bending of multilayer beam slabs lying on an elastic half-space |
| title_full_unstemmed | Bending of multilayer beam slabs lying on an elastic half-space |
| title_short | Bending of multilayer beam slabs lying on an elastic half-space |
| title_sort | bending of multilayer beam slabs lying on an elastic half space |
| topic | multilayer beam slab interaction half-space shear stress filler rigidity discreteness contact conditions regularity |
| url | http://engstroy.spbstu.ru/article/2024.130.04/ |
| work_keys_str_mv | AT mirsaidovmirziyodmirsaidovich bendingofmultilayerbeamslabslyingonanelastichalfspace AT vatinnikolaiivanovich bendingofmultilayerbeamslabslyingonanelastichalfspace AT mamasolievkazokboy bendingofmultilayerbeamslabslyingonanelastichalfspace |