The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate
The article considers the problem of embedding a rigid body into an isotropic elastic-elastic half-space through a deformable plate having properties characteristic of thin plates – elastic bodies with a thickness much smaller than other geometric dimensions and studied according to the theories of...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | deu |
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Academician I.G. Petrovskii Bryansk State University
2024-12-01
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| Series: | Naučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta |
| Subjects: | |
| Online Access: | https://ntv-brgu.ru/wp-content/arhiv/2024-N4/2024-04-05.pdf |
| _version_ | 1826899418971897856 |
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| author | Kustarev G.V. Pavlov S.A. Rusinov K.A. Gusev A.A. Novotortsev N.V. |
| author_facet | Kustarev G.V. Pavlov S.A. Rusinov K.A. Gusev A.A. Novotortsev N.V. |
| author_sort | Kustarev G.V. |
| collection | DOAJ |
| description | The article considers the problem of embedding a rigid body into an isotropic elastic-elastic half-space through a deformable plate having properties characteristic of thin plates – elastic bodies with a thickness much smaller than other geometric dimensions and studied according to the theories of Kirchhoff and Poisson. The presence of a thin plate changes the characteristics of the embedding process, since the methods applicable to solving direct indentation into the half-space cannot be used to determine the dependence of the load on deformation. The integral differential equations determining the embedding of a rigid body of finite dimensions are solved using the discretization approach. The integral transformation method made it possible to determine the loading operator, an integral part of which is the parameter of the relative stiffness of a system consisting of a plate and an elastic half-space. The relative stiffness depends on the elastic modulus and geometric parameters of the contact area and the elastic plate. The influence of the stiffness of an elastic plate on the relative stiffness of the entire system is analyzed and the results demonstrating the effect of plate stiffness on the Boussinesq problem of deformation of a half-space are presented. The solution of this problem is applicable to the practical field of scientific research on the compaction of asphalt concrete mixtures with various types of sealing working bodies, since the nature of the formation of defects in asphalt concrete coating retains scientific interest in the creation of alternative sealing equipment. |
| first_indexed | 2025-02-17T06:52:01Z |
| format | Article |
| id | doaj.art-09f28f1c1f754b10972df7fd8fc0029d |
| institution | Directory Open Access Journal |
| issn | 2413-9920 |
| language | deu |
| last_indexed | 2025-02-17T06:52:01Z |
| publishDate | 2024-12-01 |
| publisher | Academician I.G. Petrovskii Bryansk State University |
| record_format | Article |
| series | Naučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta |
| spelling | doaj.art-09f28f1c1f754b10972df7fd8fc0029d2025-01-06T10:05:48ZdeuAcademician I.G. Petrovskii Bryansk State UniversityNaučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta2413-99202024-12-0110429630210.22281/2413-9920-2024-10-04-296-302The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plateKustarev G.V.0Pavlov S.A.1Rusinov K.A.2Gusev A.A.3Novotortsev N.V.4Moscow Automobile and Road Engineering State Technical University Moscow Automobile and Road Engineering State Technical University Moscow Automobile and Road Engineering State Technical University Moscow Automobile and Road Engineering State Technical University Moscow Automobile and Road Engineering State Technical University The article considers the problem of embedding a rigid body into an isotropic elastic-elastic half-space through a deformable plate having properties characteristic of thin plates – elastic bodies with a thickness much smaller than other geometric dimensions and studied according to the theories of Kirchhoff and Poisson. The presence of a thin plate changes the characteristics of the embedding process, since the methods applicable to solving direct indentation into the half-space cannot be used to determine the dependence of the load on deformation. The integral differential equations determining the embedding of a rigid body of finite dimensions are solved using the discretization approach. The integral transformation method made it possible to determine the loading operator, an integral part of which is the parameter of the relative stiffness of a system consisting of a plate and an elastic half-space. The relative stiffness depends on the elastic modulus and geometric parameters of the contact area and the elastic plate. The influence of the stiffness of an elastic plate on the relative stiffness of the entire system is analyzed and the results demonstrating the effect of plate stiffness on the Boussinesq problem of deformation of a half-space are presented. The solution of this problem is applicable to the practical field of scientific research on the compaction of asphalt concrete mixtures with various types of sealing working bodies, since the nature of the formation of defects in asphalt concrete coating retains scientific interest in the creation of alternative sealing equipment.https://ntv-brgu.ru/wp-content/arhiv/2024-N4/2024-04-05.pdfroad rollera rigid rollerdeformation of an elastic platean embedded bodya sealing stamp |
| spellingShingle | Kustarev G.V. Pavlov S.A. Rusinov K.A. Gusev A.A. Novotortsev N.V. The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate Naučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta road roller a rigid roller deformation of an elastic plate an embedded body a sealing stamp |
| title | The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate |
| title_full | The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate |
| title_fullStr | The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate |
| title_full_unstemmed | The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate |
| title_short | The introduction of a rigid body of finite dimensions into an elastic-elastic half-space reinforced on the surface by a deformable plate |
| title_sort | introduction of a rigid body of finite dimensions into an elastic elastic half space reinforced on the surface by a deformable plate |
| topic | road roller a rigid roller deformation of an elastic plate an embedded body a sealing stamp |
| url | https://ntv-brgu.ru/wp-content/arhiv/2024-N4/2024-04-05.pdf |
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