Study On Finite Deformations Of Inflated Torus-shaped Membrane

Some industrial application sections put forward the request that investigates the rubber macromolecule material machine characteristic in recent years and hope to compute and analyze various large deformation of the membrane structure. The large deformation of thin membrane is a very important problem within non-linear finite elasticity theories, Green and Adkins advanced the elasticity theories of the rubber-like thin membrane in their research paper in 1970, and the Green Adkins, Eringen etc. have ever pointed out that the global thin membrane will lose stability in its expand process of large deformation. It is supposed that the whole radius of annulus is far larger than its radius of cross section, Kydoniefs and Spencer made use of perturbation method to study the large deformation expand problem of thin annular membrane. Under the same assumption, Hill still used perturbation method to analyze the expand deformation of thick annular membrane. All limited several parameters must be a small parameter in the above-mentioned researches of annular membrane, as a result it had a certainly limit.In this paper, I referenced a kind of large deformation shell element, the constitutive relation of Hyper-elastic material, and studied the geometrical deformation description and control equation of torus-shaped membrane. Combining currently accepted most strong finite element analysis for-and-after disposal software in the world -- MSC.Patran and strong non-linear finite element analysis software -- MSC.Marc's solver to resolve this expand deformation process of torus-shaped membrane.Through these works, I set up an appropriate finite element model, analysis and discuss this model, we can obtain that a few different material torus-shaped membrane with one node fixed and symmetrical inside pressure, we studied its structure deformation,stress distributing, deformation change curves and its thickness.This dissertation combined finite element method and computer numerical simulation technology, and analyzed that different material torus-shaped membrane with asymmetric thickness and symmetrical inside pressure would appear large deformation, stress distributing and variable thickness. It provide reference basis for the research problem of annular membrane large deformation and losing stability.