【作者】 王亮；

【导师】 张义同；

【作者基本信息】 天津大学 ， 固体力学， 2005， 硕士

【摘要】 近年来一些工业应用部门不断的提出探索橡胶高分子膜材料机械特性的要求并希望计算分析各种膜结构的大变形。薄膜大变形问题是非线性有限弹性理论中的一个重要问题,Green和Adkins于1970年在著作中提出橡胶薄膜的弹性理论,并且Green和Adkins,Eringen等曾指出球形薄膜在大变形膨胀过程中会发生失稳现象。在环面整体半径远远大于其横截面半径的假设下,Kydoniefs和Spencer应用摄动法研究了环面薄膜的大变形膨胀问题。在同样的假设下,Hill仍用摄动法分析了环面厚薄膜的膨胀变形。上述有关环面薄膜的研究中均限制了几何参数必须是一个小参数,因而具有一定的局限性。本文参考了一种大变形曲壳单元和超弹性材料的本构关系并研究了圆截面环形膜的几何、变形描述及控制方程。并利用目前世界上公认的最强大的有限元分析前后处理软件MSC.Patran与强大的非线性有限元分析软件—MSC.Marc的求解器结合在一起对环面薄膜在大变形膨胀过程进行了分析。在这些工作的基础上,通过建立合理的有限元模型,通过对模型的分析和讨论,探讨了几种不同材料环面薄膜在一节点固定的情况下受均布内力作用下结构位移变化、应力分布和某一点的位移变化曲线以及结构的厚度变化的情况从而得出了几种材料变化情况。本文将有限元方法与计算机数值模拟技术相结合,分析研究了不同材料环面薄膜在结构厚度不均匀时受到均匀内力作用以后发生大变形及变形后应力分布厚度变化情况,为环面薄膜大变形失稳研究提供了参考依据。更多还原

【Abstract】 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.更多还原