Semi-inverse solution for Saint-Venant's problem in the theory of porous elastic materials |
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| Institution: | 1. Department of Medical Physics, University of Wisconsin School of Medicine and Public Health, 1111 Highland Avenue, Madison, WI, USA 53705-2275;2. Department of Radiology, University of Wisconsin School of Medicine and Public Health, 1111 Highland Avenue, Madison, WI, USA 53705-2275;1. Key Laboratory for Beam Technology and Materials Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China;2. Beijing Radiation Center, Beijing 100875, China;3. Analytical and Testing Center, Beijing Normal University, Beijing 100875, China;1. Department of Mathematics, Soochow University, Suzhou 215006, PR China;2. Department of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, PR China;1. Université Lille Nord de France, F-59000 Lille, France;2. LG2IA, Faculté des Sciences Appliquées, TechnoParc Futura, 62400 Béthune, France;3. Université de Valenciennes et du Hainaut-Cambrésis, LAMIH, 59313 Valenciennes, France;4. Université de Valenciennes et du Hainaut-Cambrésis, TEMPO, 59313 Valenciennes, France;5. CNRS, UMR 8201, 59313 Valenciennes, France |
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| Abstract: | The purpose of this research is to study the Saint-Venant's problem for right cylinders with general cross-section made of inhomogeneous anisotropic elastic materials with voids. We reformulate the quasi-static equilibrium equations with the axial variable playing the role of a parameter. Two classes of semi-inverse solutions to Saint-Venant's problem are described in terms of five generalized plane strain problems. These classes are used in order to obtain a semi-inverse solution for the relaxed Saint-Venant's problem. An application of this results in the study of extension, bending, torsion and flexure of right circular cylinders in the case of isotropic materials is presented. |
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