The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical mode...The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical model is formulated by using the nonlinear field theory and the implicit analytical solutions are derived. Then numerical simulations are implemented to further illustrate the results and obtain some meaningful conclusions. The deformation of the lateral surface of the ring becomes larger with the increasing axial loads, the decreasing ratio of the inner and outer radii and the increasing height of the ring.展开更多
Let R be a simple Artinian ring,M<sub>m×n</sub>（R） be the set of all m×n matrices over R.GL<sub>n</sub>（R） be the set of all n×n invertible matrices over R.Let A<sup>T&...Let R be a simple Artinian ring,M<sub>m×n</sub>（R） be the set of all m×n matrices over R.GL<sub>n</sub>（R） be the set of all n×n invertible matrices over R.Let A<sup>T</sup> be the transpose matrix ofA∈M<sub>m×n</sub>（R）.By the Wedderburn-Artin theorem,R be isomorphic to a total matrix ringM<sub>s×s</sub>（D） over a division ring D.Let α→（α）<sub>D</sub> be an isomorphism of R onto M<sub>s×s</sub>（D）, if展开更多
基金supported by the National Natural Science Foundation of China (Nos. 10872045, 10721062 and 10772104)the Program for New Century Excellent Talents in University (No. NCET-09-0096)the Fundamental Research Funds for the Central Universities
文摘The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical model is formulated by using the nonlinear field theory and the implicit analytical solutions are derived. Then numerical simulations are implemented to further illustrate the results and obtain some meaningful conclusions. The deformation of the lateral surface of the ring becomes larger with the increasing axial loads, the decreasing ratio of the inner and outer radii and the increasing height of the ring.
基金Supported by the NSF of Hunan Provincethe Science and Technology Development Foundation of Xiangtan Polytechnic University
文摘Let R be a simple Artinian ring,M<sub>m×n</sub>（R） be the set of all m×n matrices over R.GL<sub>n</sub>（R） be the set of all n×n invertible matrices over R.Let A<sup>T</sup> be the transpose matrix ofA∈M<sub>m×n</sub>（R）.By the Wedderburn-Artin theorem,R be isomorphic to a total matrix ringM<sub>s×s</sub>（D） over a division ring D.Let α→（α）<sub>D</sub> be an isomorphism of R onto M<sub>s×s</sub>（D）, if
