基于解析试函数的内参型广义协调膜元  

A GENERALIZED CONFORMING PLANE ELEMENT WITH INTERNAL PARAMETERS BASED ON ANALYTICAL TRIAL FUNCTIONS

作　　者：傅向荣[1] 龙驭球[2] 袁明武[1] 岑松[3] 

机构地区：[1]北京大学力学与工程科学系,北京100871 [2]清华大学土木工程系,北京100084 [3]清华大学工程力学系,北京100084

出　　处：《工程力学》2006年第1期1-5,共5页Engineering Mechanics

基　　金：国家自然科学基金(10272063);高等学校博士学科点专项科研基金(20020003044);清华大学基础研究基金(JC2002003);全国优秀博士论文作者专项基金(200242);中国博士后科学基金(2003033071)

摘　　要：利用解析试函数法构造一个内参型四结点八自由度广义协调膜元。根据弹性力学平面问题的控制方程和艾雷应力函数,求出问题完备的基本解析解,然后用其作为试函数并采用广义协调条件来构造单元:ATF-GCQ4X。该单元采用了14个解析试函数构造了应变二次完备的内部场,同时引入6个附加边界位移模式,采用平衡力系为权函数构造相应的广义协调条件。数值算例表明,该类内参型单元能在不提高单元结点自由度的情况下提高单元精度,并显示出良好的收敛特性。Based on the analytical trial functions, a 4-node 8 degrees-of-freedom generalized conforming plane element with internal parameters is developed in this paper. From the governing equations of the elastic plane problem and the Airy stress function, the complete basic analytical solutions are derived and used as the trial functions to formulate the element： ATF-GCQ4X. Fourteen analytical trial functions form the second order complete inner field for strain while six additional boundary displacement modules are used as internal parameters. Balance forces are used to form the generalized conforming equations. Numerical examples show that the proposed element with internal parameters can enhance the precision without increasing degree-of-freedom, and satisfactory convergence rate is achieved.

关 键 词：力学 有限元 新方法 解析试函数 内参 

分 类 号：TB115[理学—数学]