| Abstract: | In the present paper the radiation conditions of the Sommerfield type for a linear homogeneous and isotropic micropolar elasticity are discussed. A regular solution (u,  ) of the fundamental system of field equations in an infinite domain has been defined using the radiation conditions for % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaacIcacaWG1bWaaSbaaSqaaiaacIcacaWG% WbGaaiykaaqabaGccaGGSaGaey4kaSIaeqy1dO2aaSbaaSqaaiaacI% cacaWGWbGaaiykaaqabaGccaGGPaaaaa!4834!\(u_{(p)} , + \varphi _{(p)} )\] and % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaacIcacaWG1bWaaSbaaSqaaiaacIcacaWG% ZbGaaiykaaqabaGccaGGSaGaey4kaSIaeqy1dO2aaSbaaSqaaiaacI% cacaWGZbGaaiykaaqabaGccaGGPaaaaa!483A!\(u_{(s)} , + \varphi _{(s)} )\], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaadwhacqGH9aqpcaWG1bWaaSbaaSqaaiaa% cIcacaWGWbGaaiykaaqabaGccqGHRaWkcaWG1bWaaSbaaSqaaiaacI% cacaWGZbGaaiykaaqabaGccaGGSaGaaeiiaiabgEGirlabgEna0kaa% dwhadaWgaaWcbaGaaiikaiaadchacaGGPaaabeaakiabg2da9iaaic% dacaGGSaGaaeiiaiabgEGirhrbmv3yPrwyGm0BUn3BSvgaiyGacaWF% 1bWaaSbaaSqaaGqaciaa+HcacaGFZbGaa4xkaaqabaGccqGH9aqpca% aIWaGaaiilaiaabccacqaHvpGAcqGH9aqpcqaHvpGAdaWgaaWcbaGa% aiikaiaadchacaGGPaaabeaakiabgUcaRiabew9aQnaaBaaaleaaca% GGOaGaam4CaiaacMcaaeqaaOGaaiilaiaabccacqGHhis0cqGHxdaT% cqaHvpGAdaWgaaWcbaGaaiikaiaadchacaGGPaaabeaakiabg2da9i% aaicdacaGGSaGaaeiiaiabgEGirlabew9aQnaaBaaaleaacaqGOaGa% ae4CaiaabMcaaeqaaOGaeyypa0JaaGimaaaa!809B!\u = u_{(p)} + u_{(s)} ,{\text{ }}\nabla \times u_{(p)} = 0,{\text{ }}\nabla u_{(s)} = 0,{\text{ }}\varphi = \varphi _{(p)} + \varphi _{(s)} ,{\text{ }}\nabla \times \varphi _{(p)} = 0,{\text{ }}\nabla \varphi _{{\text{(s)}}} = 0\], and formulae of the Betti type for an infinite domain with a cavity have been derived.
Zusammenfassung Betrachtet werden die Ausstrahlungsbedingungen der Sommerfeldschen Art für lineare homogene mikropolare Elastizitätstheorie. Die reguläre Lösung (u,  ) der grundlegenden Gleichungen für einen unendlichen Raum wird mit Hilfe der Bedingungen für Paare % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaacIcacaWG1bWaaSbaaSqaaiaacIcacaWG% WbGaaiykaaqabaGccaGGSaGaey4kaSIaeqy1dO2aaSbaaSqaaiaacI% cacaWGWbGaaiykaaqabaGccaGGPaaaaa!4834!\(u_{(p)} , + \varphi _{(p)} )\] und % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaacIcacaWG1bWaaSbaaSqaaiaacIcacaWG% ZbGaaiykaaqabaGccaGGSaGaey4kaSIaeqy1dO2aaSbaaSqaaiaacI% cacaWGZbGaaiykaaqabaGccaGGPaaaaa!483A!\(u_{(s)} , + \varphi _{(s)} )\] definiert, wobei % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbnL2yY9% 2CVzgDGmvyUnhitvMCPzgarmWu51MyVXgaruWqVvNCPvMCG4uz3bqe% fqvATv2CG4uz3bIuV1wyUbqee0evGueE0jxyaibaieYlf9irVeeu0d% Xdh9vqqj-hEeeu0xXdbba9frFf0-OqFfea0dXdd9vqaq-JfrVkFHe9% pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaaca% qabeaadaabauaaaOqaaiaadwhacqGH9aqpcaWG1bWaaSbaaSqaaiaa% cIcacaWGWbGaaiykaaqabaGccqGHRaWkcaWG1bWaaSbaaSqaaiaacI% cacaWGZbGaaiykaaqabaGccaGGSaGaaeiiaiabgEGirlabgEna0kaa% dwhadaWgaaWcbaGaaiikaiaadchacaGGPaaabeaakiabg2da9iaaic% dacaGGSaGaaeiiaiabgEGirhrbmv3yPrwyGm0BUn3BSvgaiyGacaWF% 1bWaaSbaaSqaaGqaciaa+HcacaGFZbGaa4xkaaqabaGccqGH9aqpca% aIWaGaaiilaiaabccacqaHvpGAcqGH9aqpcqaHvpGAdaWgaaWcbaGa% aiikaiaadchacaGGPaaabeaakiabgUcaRiabew9aQnaaBaaaleaaca% GGOaGaam4CaiaacMcaaeqaaOGaaiilaiaabccacqGHhis0cqGHxdaT% cqaHvpGAdaWgaaWcbaGaaiikaiaadchacaGGPaaabeaakiabg2da9i% aaicdacaGGSaGaaeiiaiabgEGirlabew9aQnaaBaaaleaacaqGOaGa% ae4CaiaabMcaaeqaaOGaeyypa0JaaGimaaaa!809B!\u = u_{(p)} + u_{(s)} ,{\text{ }}\nabla \times u_{(p)} = 0,{\text{ }}\nabla u_{(s)} = 0,{\text{ }}\varphi = \varphi _{(p)} + \varphi _{(s)} ,{\text{ }}\nabla \times \varphi _{(p)} = 0,{\text{ }}\nabla \varphi _{{\text{(s)}}} = 0\] ist. Es wird gezeigt, dass derartige reguläre Lösung mit Hilfe der Formel Bettischer Art für einem unendlichen Raum mit einem Hohlraum dargestellt werden kann. |
