用四边形平面应力单元进行平面梁的几何非线性分析  

The geometrical non-linearity analysis for plane beam with quadrilateral plane stress element

作　　者：邓继华[1] 蔡松柏[2] 

机构地区：[1]长沙理工大学桥梁与结构工程学院,湖南长沙410076 [2]湖南师范大学资源与环境学院,湖南长沙410081

出　　处：《长沙理工大学学报（自然科学版）》2007年第2期32-35,共4页Journal of Changsha University of Science and Technology:Natural Science

基　　金：交通部西部交通建设科研资助项目(200431878518)

摘　　要：采用共旋坐标法导出了四边形平面应力单元在大转动、小应变条件下的几何非线性单元切线刚度矩阵,在此基础上编制了相应的有限元程序.为了验证其正确性,用在悬臂端作用有集中力的平面悬臂梁来进行校核.计算结果表明,随着单元网格的加密,计算值越来越趋近于解析值,且计算值对单元形状的改变不是很敏感.由此说明所推导的四方形平面应力单元在大转动、小应变条件下的几何非线性单元切线刚度矩阵是正确的,在类似问题的分析中有一定的参考价值.A tangent stiffness matrix for quadrilateral plane stress element under large rotation with small strain is proposed in this paper. Based on this theory, a FORTRAN computer program has been developed. A cantilever beam with a single concentrated load at the end is employed to examine its accuracy. The calculated results demonstrate that the calculation values gradually reach to the analytic values with the increasing of the element mesh density. Moreover, the calculated values are not sensitive to the change of the element geometry. It is concluded that the deduced element is accurate and suitable to deal with the similar issues.

关 键 词：平面应力单元 共旋坐标法 平面梁 几何非线性 

分 类 号：U441.5[建筑科学—桥梁与隧道工程]