On Equilibrium Problem for T-Shape Elastic Structure
This paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of the elastic plate; in the second case, contact oc...
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MDPI AG
2025-01-01
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| author | Alexander Khludnev |
| author_facet | Alexander Khludnev |
| author_sort | Alexander Khludnev |
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| description | This paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of the elastic plate; in the second case, contact occurs between two elastic bodies. The elastic plate may contain a thin rigid delaminated inclusion. Neumann-type boundary conditions are considered at the external boundary of the plate. The existence of a solution to the considered problems is proven. A sufficient and necessary condition imposed onto the external forces for the solvability of the problems is found. Passages to the limit with respect to the rigidity parameter of the elastic beam are justified. For all problems, we analyze variational statements as well as differential ones. |
| format | Article |
| id | doaj-art-db1a643a1f7242b594738a1c5fa97a21 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-db1a643a1f7242b594738a1c5fa97a212025-01-24T13:22:16ZengMDPI AGAxioms2075-16802025-01-011414910.3390/axioms14010049On Equilibrium Problem for T-Shape Elastic StructureAlexander Khludnev0Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk 630090, RussiaThis paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of the elastic plate; in the second case, contact occurs between two elastic bodies. The elastic plate may contain a thin rigid delaminated inclusion. Neumann-type boundary conditions are considered at the external boundary of the plate. The existence of a solution to the considered problems is proven. A sufficient and necessary condition imposed onto the external forces for the solvability of the problems is found. Passages to the limit with respect to the rigidity parameter of the elastic beam are justified. For all problems, we analyze variational statements as well as differential ones.https://www.mdpi.com/2075-1680/14/1/49T-shape structureelastic platevolume and thin inclusionssolution existenceasymptotic analysisNeumann boundary condition |
| spellingShingle | Alexander Khludnev On Equilibrium Problem for T-Shape Elastic Structure Axioms T-shape structure elastic plate volume and thin inclusions solution existence asymptotic analysis Neumann boundary condition |
| title | On Equilibrium Problem for T-Shape Elastic Structure |
| title_full | On Equilibrium Problem for T-Shape Elastic Structure |
| title_fullStr | On Equilibrium Problem for T-Shape Elastic Structure |
| title_full_unstemmed | On Equilibrium Problem for T-Shape Elastic Structure |
| title_short | On Equilibrium Problem for T-Shape Elastic Structure |
| title_sort | on equilibrium problem for t shape elastic structure |
| topic | T-shape structure elastic plate volume and thin inclusions solution existence asymptotic analysis Neumann boundary condition |
| url | https://www.mdpi.com/2075-1680/14/1/49 |
| work_keys_str_mv | AT alexanderkhludnev onequilibriumproblemfortshapeelasticstructure |