Green's function solution and displacement potentials for Transformed Transversely Isotropic materials |
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| Institution: | 1. Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, 39005 Santander, Spain;2. Basque Center for Applied Mathematics (BCAM), Alameda Mazarredo 14, E-48009 Bilbao, Basque Country, Spain;3. IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Basque Country, Spain;1. Faculty of Engineering, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran;2. Department of Materials Science & Engineering, Missouri University of Science & Technology, Rolla, MO 65409, USA;1. School of Mechano-Electronic Engineering, Xidian University, Xi’an, 710071 Shaanxi, PR China;2. Key Laboratory of Mechanics on Disaster and Environment in Western China (Lanzhou University), Ministry of Education, Lanzhou, 730000 Gansu, PR China;1. Université Mouloud Mammeri de Tizi-Ouzou, Département Génie Civil, Algeria;2. Université d׳Avignon et des Pays de Vaucluse (UAPV), UMR1114 EMMAH, Faculté des Sciences, 33 rue Louis Pasteur, F-84914 Avignon, France;3. INRA, UMR1114 EMMAH, F-84914 Avignon, France |
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| Abstract: | A totally non-degenerate expression for the Green's function of infinite Transversely Isotropic (TI) materials is first deduced from the solutions given by Pan and Chou Pan, Y.-C., Chou, T.-W., 1976. Point force solution for an infinite transversely isotropic solid. Trans. ASME, J. Appl. Mech. 43 (4), 608–612]. Then this solution and also the displacement potentials for TI materials are extended by a linear transformation to a larger family of anisotropic materials (Transformed Transversely Isotropic or TraTI materials). This family depends on 12 independent parameters and contains non-orthotropic materials and in this way a first explicit analytical solution for the Green's function for a non-orthotropic material is obtained. The TraTI materials which have orthotropic Symmetry (StraTI materials) constitute a sub-family depending on 6 independent parameters in the symmetry basis of the material. These materials present a 3D anisotropy (different stiffnesses in three orthogonal directions). General displacement potentials and the Green's function solution for STraTI materials can be deduced by a simple change and introducing one additional parameter in the well-known TI solutions. |
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