摘要
本研究将新近发展起来的有限元线法应用于非线性问题,分析求解了若干具有代表性的模型问题,探讨了统一的求解模式及相应的处理手段。作为这一系列工作的首例,本文将该法应用于薄膜大挠度这一几何非线性模型问题,对任意形状的薄膜作了理论公式推导,通过对几种典型形状薄膜的具体数值计算,揭示了该类问题存在极限变形状态这一重要特性。数值算例的精确性与可靠性以及求解的高效性表明,本法是求解这类几何非线性问题的高效能的方法。
The present investigation extends the application of the newly
developed finite element method of lines (FEMOL) to nonlinear problems by
solving a series of representative nonlinear model problems in a fashion of
unified formulation and solution. This is the first paper in this series,and is
concerned with the FEMOL solution of a geometrically nonlinear problem--
large deflection of membranes.FEMOL formulation for membranes on arbitrary domains is derived. Numerical results computed from a number of membranes of different shapes show an important property in this class of problems, i.e. the existence of a limit deformation state.The solution accuracy, reliability and efficiency exhibit that the method is highly effective and powerful for this kind of geometrically nonlinear problem.
出处
《工程力学》
EI
CSCD
1993年第1期1-9,共9页
Engineering Mechanics
基金
国家自然科学金基资助项目
关键词
有限元线法
非线性
薄膜
大挠度
The Finite Element Method of Lines, Nonlinearity, Model Problems, Unified Solution, Large Deflection of Membrane
