Notes on the nonlinearly elastic Boussinessq problem

Simmonds, J. G. ; Warne, P. G.
Springer
Published 1994
ISSN:
1573-2681
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Physics
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.
Type of Medium:
Electronic Resource
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
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timestamp 2024-05-06T09:55:43.947Z
titel Notes on the nonlinearly elastic Boussinessq problem
titel_suche Notes on the nonlinearly elastic Boussinessq problem
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