The symmetry principle in continuum mechanics |
| |
| Institution: | 1. School of Civil and Environmental Engineering, University of Technology, Sydney, Post Box 129, Broadway, NSW 2007, Australia;2. College of Environmental Science and Engineering, State Environmental Protection Engineering Center for Pollution Treatment and Control in Textile Industry, Donghua University, Shanghai 201620, China;3. School of Civil, Environmental and Architectural Engineering, Korea University, 1-5 Ga, Anam-Dong, Seongbuk-Gu, Seoul 136-713, Republic of Korea;4. King Abdullah University of Science and Technology (KAUST), Water Desalination and Reuse Center (WDRC), Division of Biological & Environmental Science & Engineering (BESE), 4700, Thuwal 23955-6900, Saudi Arabia;1. Mathematical Institute, Radcliffe Observatory Quarter, Oxford, OX2 6GG, UK;2. Pall Life Sciences, 20 Walkup Drive, Westborough, MA 01581, USA;3. School of Mathematics and Statistics, University of Glasgow, G12 8QW, UK;1. Department of Biomedical and Chemical Engineering, Syracuse University, Syracuse, NY 13244, USA;2. Department of Paper and Bioprocess Engineering, Empire State Paper Research Institute, State University of New York, College of Environmental Science and Forestry, Syracuse, NY 13210, USA;1. Université de Toulouse, UPS; UMR 152 Pharma-Dev, Université Toulouse 3, Faculté des Sciences Pharmaceutiques, F-31062 Toulouse Cedex 09, France;2. Institut de Recherche pour le Développement (IRD), UMR 152 Pharma-Dev, F-31062 Toulouse Cedex 09, France;3. LAAS-CNRS, 7 Avenue du Colonel Roche, F-31077 Toulouse Cedex 4, France;1. Department of Mathematics, The University of Tulsa, Tulsa, OK, United States;2. EPFL, SB Institute of Mathematics, Station 8, Lausanne, Switzerland;3. Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca'' Foscari Venezia, Venezia Mestre, Italy;4. Department of Complex Analysis and Potential Theory, Institute of Mathematics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine |
| |
| Abstract: | For problems of the mechanics of an anisotropic inhomogeneous continuum, theorems are given concerning the uninterrupted symmetrical and antisymmetrical analytical continuation of the solution through the plane part of the boundary surface of the medium. Theorems are given for two types of mechanics problem; in the first of these both symmetrical and antisymmetrical continuations of the solution are allowed, while in the second only symmetrical continuation of the solution is allowed. Problems of the first type include problems which are reduced to linear thermoelastic dynamic differential equations of motion of an inhomogeneous anisotropic medium possessing a plane of elastic symmetry, to linear thermoelastic dynamic differential equations of motion of an inhomogeneous Cosserat medium, to non-linear differential equations describing the static elastoplastic stress state of a plate, etc. The second type includes problems which are reduced to non-linear differential equations describing geometrically non-linear strains of shells, to Navier–Stokes equations, etc. These theorems extend the principle of mirror reflection (the Riemann–Schwartz principle of symmetry) to linear and non-linear equations of continuum mechanics. The uninterrupted continuation of the solutions is used to solve problems of the equilibrium state of bodies of complex shape. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
