Uniformity of stresses inside an elliptic inclusion in finite plane elastostatics |
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| Institution: | 1. Department of Mechanical Engineering, University of Alberta, 4-9 Mechanical Engineering Bldg., Edmonton, Alberta, Canada T6G 2G8;2. Department of Mechanical and Manufacturing Engineering, University of Calgary, Alberta, Canada;1. Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, PR China;2. HeFei KEYE Electrical Physical Equipment Co., Ltd., PR China;1. Institute of Plasma Physics of Chinese Academy of Sciences, Hefei 230031, PR China;2. Princeton Plasma Physics Laboratory, PO Box 451, Princeton, NJ 08543, United States;1. ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, 13067 St. Paul Lez Durance Cedex, France;2. Assystem EOS, 117 rue Jacquard, 84120 Pertuis, France;3. Sogeti High Tech, RE2, 180 rue René Descartes, Le Millenium – Bat C, 13857 Aix en Provence, France;4. SOM Calcul – Groupe ORTEC, 121 ancien Chemin de Cassis – Immeuble Grand Pré, 13009 Marseille, France;1. National Fusion Research Institute, Daejeon, South Korea;2. Ulsan National Institute of Science and Technology, Ulsan, South Korea |
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| Abstract: | We consider an elastic inclusion embedded in a particular class of harmonic materials subjected to uniform remote stress. Using complex variable techniques, we show that if the Piola stress within the inclusion is uniform, the inclusion is necessarily an ellipse except in the special case when the (uniform) remote stress assumes a particular form. In addition, we obtain the complete solution for an elliptic inclusion with uniform interior stress for any uniform remote stress distribution. |
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