On singularities associated with the curvilinear anisotropic elastic symmetries |
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| Institution: | 1. Department of Biomedical Engineering, The New York Center for Biomedical Engineering, The School of Engineering of the City College, The Graduate School of the City University of New York, NY, USA;2. Department of Mechanical Engineering, The New York Center for Biomedical Engineering, The School of Engineering of the City College, The Graduate School of the City University of New York, NY, USA;3. Dipartimento di Scienza delle Costruzioni, Facoltà di Ingegneria, Università di Napoli, “Federico II”, Italy;1. Département d’Energétique et de Mécanique des Fluides, Faculté de Physique, USTHB, BP 32 El-Alia 16111 Bab-Ezzouar Alger, Algeria;2. Département de Physique, École Préparatoire en Sciences et Technique d’Alger, BP 374 Place des Martyres 16000, Alger, Algeria;3. Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA;4. LPMT, Université de Haute-Alsace, 11 rue Alfred Werner, 68093 Mulhouse Cedex, France;5. Department of Industrial Engineering, Faculty of Engineering, Fayoum University, Fayoum 63514, Egypt;6. LEMTA, Université de Lorraine, 2 Avenue de la Fôret de Haye, BP 90161, 54505 Vandoeuvre-lès-Nancy Cedex, France;1. Department of Civil Engineering and Architecture, University of Catania, Italy;2. Department of Structural and Geotechnical Engineering, University of Rome La Sapienza, Italy;3. Department of Architecture, University of Roma 3, Italy;4. International Research Center on Mathematics and Mechanics of Complex System, M&MOCS, Cisterna di Latina, Italy;1. Department of Applied Mathematics and Systems Analysis, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation;2. Cybernetic Institute, National Research Tomsk Polytechnic University, 30 Lenin Avenue, 634050 Tomsk, Russian Federation;3. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., 90-924 Lodz, Poland;4. Department of Vehicles, Warsaw University of Technology, 84 Narbutta Str., 02-524 Warsaw, Poland;5. Department of Mathematics and Modeling, Saratov State Technical University, 77 Politehnicheskaya Str., 410054 Saratov, Russian Federation |
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| Abstract: | The objective of this paper is to describe a different approach to modeling the material symmetry associated with singularities that can occur in curvilinear anisotropic elastic symmetries. In this analysis, the intrinsic non-linearity of a cylindrically anisotropic problem is demonstrated. We prove that a simple homogenization process applied to a representative volume element containing the cylindrical anisotropic singularity removes the singularity. This geometric and interpretive approach is an aid to better modeling of material symmetry associated with these singularities. |
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