Notes on the nonlinearly elastic Boussinessq problem
| ISSN: |
1573-2681
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| Source: |
Springer Online Journal Archives 1860-2000
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| Topics: |
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Physics
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| Notes: |
Abstract The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot.
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| Type of Medium: |
Electronic Resource
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| URL: |
| _version_ | 1798296667367145473 |
|---|---|
| autor | Simmonds, J. G. Warne, P. G. |
| autorsonst | Simmonds, J. G. Warne, P. G. |
| book_url | http://dx.doi.org/10.1007/BF00042426 |
| datenlieferant | nat_lic_papers |
| hauptsatz | hsatz_simple |
| identnr | NLM193768577 |
| issn | 1573-2681 |
| journal_name | Journal of elasticity |
| materialart | 1 |
| notes | Abstract The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot. |
| package_name | Springer |
| publikationsjahr_anzeige | 1994 |
| publikationsjahr_facette | 1994 |
| publikationsjahr_intervall | 8009:1990-1994 |
| publikationsjahr_sort | 1994 |
| publisher | Springer |
| reference | 34 (1994), S. 69-82 |
| search_space | articles |
| shingle_author_1 | Simmonds, J. G. Warne, P. G. |
| shingle_author_2 | Simmonds, J. G. Warne, P. G. |
| shingle_author_3 | Simmonds, J. G. Warne, P. G. |
| shingle_author_4 | Simmonds, J. G. Warne, P. G. |
| shingle_catch_all_1 | Simmonds, J. G. Warne, P. G. Notes on the nonlinearly elastic Boussinessq problem Abstract The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot. 1573-2681 15732681 Springer |
| shingle_catch_all_2 | Simmonds, J. G. Warne, P. G. Notes on the nonlinearly elastic Boussinessq problem Abstract The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot. 1573-2681 15732681 Springer |
| shingle_catch_all_3 | Simmonds, J. G. Warne, P. G. Notes on the nonlinearly elastic Boussinessq problem Abstract The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot. 1573-2681 15732681 Springer |
| shingle_catch_all_4 | Simmonds, J. G. Warne, P. G. Notes on the nonlinearly elastic Boussinessq problem Abstract The nonlinearly elastic Boussinesq problem is to find the deformation produced in a homogeneous, isotropic, elastic half space by a point force normal to the undeformed boundary, using the exact equations of elasticity for an incompressible or compressible material. First we derive the governing equations from the Principle of Stationary Potential Energy and then we examine some of the implications of the conservation laws of elastostatics when applied to the entire half space, assuming that the well-known linear Boussinesq solution is valid at large distances from the point load. Next, we hypothesize asymptotic forms for the solutions near the point load and, finally, we seek solutions for two specific materials: an incompressible, generalized neo-Hookean (power-law) material introduced by Knowles and a compressible Blatz-Ko material. We find that the former, if sufficiently stiffer than the conventional neo-Hookean material, can support a finite deflection under the point load, but that the latter cannot. 1573-2681 15732681 Springer |
| shingle_title_1 | Notes on the nonlinearly elastic Boussinessq problem |
| shingle_title_2 | Notes on the nonlinearly elastic Boussinessq problem |
| shingle_title_3 | Notes on the nonlinearly elastic Boussinessq problem |
| shingle_title_4 | Notes on the nonlinearly elastic Boussinessq problem |
| sigel_instance_filter | dkfz geomar wilbert ipn albert fhp |
| source_archive | Springer Online Journal Archives 1860-2000 |
| timestamp | 2024-05-06T09:55:43.947Z |
| titel | Notes on the nonlinearly elastic Boussinessq problem |
| titel_suche | Notes on the nonlinearly elastic Boussinessq problem |
| topic | ZL U |
| uid | nat_lic_papers_NLM193768577 |