基于四边形面积坐标的平面单元解析试函数法  

Analytical trial function method for plane elements based on quadrilateral area coordinate theory

作　　者：陈晓明[1] 岑松[1] 

机构地区：[1]清华大学航天航空学院,北京100084

出　　处：《清华大学学报（自然科学版）》2008年第2期289-293,共5页Journal of Tsinghua University(Science and Technology)

基　　金：国家自然科学基金资助项目(10502028);高等学校全国优秀博士论文作者专项基金资助项目(200242)

摘　　要：在四边形面积坐标QAC-II的基础上,建立了弹性力学平面问题的面积坐标解析试函数方法。该方法使面积坐标理论和解析试函数法这2个并行发展的有限元方法的研究工具得以有机结合,克服了直角坐标解析试函数法整体坐标系带来的单元方向性问题。在此基础上构造了具有显式刚度阵的平面四节点单元AATF4和五节点单元AATF5,这2个单元分别包含8项和10项试探函数,不需要增加内参位移场即可以精确模拟纯弯场,并克服了MacNeal梁的梯形闭锁问题。这2个单元的综合性能表明,面积坐标解析试函数是一个构造单元的有效工具。An analytical trial function method （ATF） was developed based on the. quadrilateral area coordinate system （QAC-Ⅱ） for plane elements （ACATF）. These two powerful tools were combined to develop accurate, robust elements, to overcome problems induced by the Cartesian coordinate system in the ATF method so that the QAC method can be more widely used. The ACATF method was used to develop a 4-node plane element, AATF4, and a 5-node plane element AATF5, with explicit stiffness matrices. Each of these two elements has the least number of possible terms in the trial function which is equal to their DOFs. Numerical results show that they are free of the trapezoidal locking of MacNeal＇s beam element and can give exact solutions for pure bending problems. The success of these elements showed that the ACATF method is an efficient tool for developing elements.

关 键 词：面积坐标 解析试函数 平面单元 网格畸变 

分 类 号：TU32[建筑科学—结构工程]