ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE
The analysis of stress-strain state of a rigid wall in an elastic weighty half-plane with a broken outline is carried out. To this end, the auxiliary problem of displacements definition in an elastic weighty quarter-plane was solved. Ritz method derived a formula to determine the displacements of el...
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Belarusian National Technical University
2016-12-01
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| Series: | Наука и техника |
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| Online Access: | https://sat.bntu.by/jour/article/view/962 |
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| author | K. V. Dmitrieva |
| author_facet | K. V. Dmitrieva |
| author_sort | K. V. Dmitrieva |
| collection | DOAJ |
| description | The analysis of stress-strain state of a rigid wall in an elastic weighty half-plane with a broken outline is carried out. To this end, the auxiliary problem of displacements definition in an elastic weighty quarter-plane was solved. Ritz method derived a formula to determine the displacements of elastic flat wedge boundaries in view of its own weight. On the basis of the received expressions the algorithm of displacements definition of a crack in an elastic weighty half-plane with a broken outline is developed. Analytical calculation of a rigid vertical wall located in an elastic weighty half-plane under the influence of a horizontal load, carried out by two methods: by Zhemochkin's method and finite difference method. In the problem statement an elastic half-plane is considered a model of the soil medium, therefore, only compressive normal stresses can arise on the connection of the wall with the elastic base. This assumption implies occurrence of discontinuities soil medium, and leads for the wall to an emergence of two dividing points of boundary conditions. The determination of the boundaries contact of the wall with the elastic half-plane, are not known in advance, is performed by iteratively way at each step set the position of dividing points of boundary conditions and the system of canonical equations of a corresponding method is written. If tensile stresses appear in wall-base contact and/or there is overlap of the crack edges occurs, then proceeds to the next iteration. Analysis of the results shows that the bending moment and shear forces in sections of the rigid wall in a broken weighty half-plane differ slightly from the same diagrams constructed for a rigid wall in an elastic weightless half-plane. The verification of the results of analytical calculation with the results received by using the LIRA 9.6 that implements the finite element method is obtained. The calculation results for the rigid wall in an elastic weighty half-plane obtained by analytical methods, qualitatively consistent with the results based on LIRA 9.6. |
| format | Article |
| id | doaj-art-5dbbb2bfc269404fb234c3f7a2dbd8e3 |
| institution | OA Journals |
| issn | 2227-1031 2414-0392 |
| language | Russian |
| publishDate | 2016-12-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Наука и техника |
| spelling | doaj-art-5dbbb2bfc269404fb234c3f7a2dbd8e32025-08-20T02:18:16ZrusBelarusian National Technical UniversityНаука и техника2227-10312414-03922016-12-0115649350310.21122/2227-1031-2016-15-6-493-503916ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANEK. V. Dmitrieva0Belarusian national technical UniversityThe analysis of stress-strain state of a rigid wall in an elastic weighty half-plane with a broken outline is carried out. To this end, the auxiliary problem of displacements definition in an elastic weighty quarter-plane was solved. Ritz method derived a formula to determine the displacements of elastic flat wedge boundaries in view of its own weight. On the basis of the received expressions the algorithm of displacements definition of a crack in an elastic weighty half-plane with a broken outline is developed. Analytical calculation of a rigid vertical wall located in an elastic weighty half-plane under the influence of a horizontal load, carried out by two methods: by Zhemochkin's method and finite difference method. In the problem statement an elastic half-plane is considered a model of the soil medium, therefore, only compressive normal stresses can arise on the connection of the wall with the elastic base. This assumption implies occurrence of discontinuities soil medium, and leads for the wall to an emergence of two dividing points of boundary conditions. The determination of the boundaries contact of the wall with the elastic half-plane, are not known in advance, is performed by iteratively way at each step set the position of dividing points of boundary conditions and the system of canonical equations of a corresponding method is written. If tensile stresses appear in wall-base contact and/or there is overlap of the crack edges occurs, then proceeds to the next iteration. Analysis of the results shows that the bending moment and shear forces in sections of the rigid wall in a broken weighty half-plane differ slightly from the same diagrams constructed for a rigid wall in an elastic weightless half-plane. The verification of the results of analytical calculation with the results received by using the LIRA 9.6 that implements the finite element method is obtained. The calculation results for the rigid wall in an elastic weighty half-plane obtained by analytical methods, qualitatively consistent with the results based on LIRA 9.6.https://sat.bntu.by/jour/article/view/962contact problemplane strainzhemochkin's methodconstructive nonlinearity |
| spellingShingle | K. V. Dmitrieva ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE Наука и техника contact problem plane strain zhemochkin's method constructive nonlinearity |
| title | ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE |
| title_full | ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE |
| title_fullStr | ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE |
| title_full_unstemmed | ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE |
| title_short | ANALYSIS OF A RIGID WALL IN AN ELASTIC WEIGHTY HALF-PLANE |
| title_sort | analysis of a rigid wall in an elastic weighty half plane |
| topic | contact problem plane strain zhemochkin's method constructive nonlinearity |
| url | https://sat.bntu.by/jour/article/view/962 |
| work_keys_str_mv | AT kvdmitrieva analysisofarigidwallinanelasticweightyhalfplane |