The Boundary Value Problems For A Class Of Nonlinear Elastic Mechanics Equations

Based on the theory of finite deformation for nonlinear continuum mechanics, theproblem of finite deformation of the structures that have two incompressible neo-Hookeanrectangular rubber rings is examined, where the rings are subjected to the axial compressionloads at its two ends. Firstly, in the case of the assumption that the cross section of the rubberring along the axial direction is still planar and perpendicular to the axis after the deformation,and the structure is static in the deformation process, the reasonable mathematic model isproposed for above-mentioned problem and assumption. Then the implicit solutions arederived by using the inverse method and the incompressibility condition of material. Somemeaningful conclusions are obtained by numerical simulations. The main works are asfollows:1In chapter3, the problem of finite deformation of the structures that have tworectangular rubber rings is studied. Through the qualitative analysis of solutions, the influenceon the deformation of axial loads and structure parameters is discussed, as well as the changeof the axial compression ratio. With the increase of axial loads, or the decrease of the inner toouter radial ratio, or the increasing width of the rings, the expansion of its outer surface alongthe radial direction is more and more obvious. It is proved that the axial compression ratio isthe biggest at the two ends; however, it is the smallest at the central cross-section of the rings.The axial compression ratio is also influenced by axial loads and structure parameters.