摘要
以基线力为状态变量,构造几何非线性问题单元的余能,该余能包括变形部分和转动部分.利用高玉臣提出的弹性大变形余能原理,以Lagrange乘子法松弛单元域内的平衡条件,得到了一个以基线力表达的修正的余能原理.在假设平面单元每一个边上的力为均匀分布的条件下,推导出一种几何非线性平面4节点有限元模型.运用MATLAB语言编制出相应的非线性有限元分析程序.数值算例结果表明该模型具有良好的性能.
Using the base line forces as fundamental variables, the complementary energy of an element with geometrical nonlinearity is constructed, which contains both deformation part and rotation part. Based on the complementary energy principle for large elastic deformation by Gao, the equilibrium condi- tions are released by the Lagrange multiplier method, and a modified complementary energy principle related to the base line forces is obtained. The 4-node plane element model with geometrical nonlinearity is derived by assuming uniform stress distribution on each faces of the element. A nonlinear finite element code is developed. Numerical results show that this model works very well.
出处
《固体力学学报》
CAS
CSCD
北大核心
2008年第4期365-372,共8页
Chinese Journal of Solid Mechanics
基金
北京市教委科技发展计划基金(KM200510005016)
北京市属市管高校人才强教计划基金(05004999200602)资助
关键词
几何非线性
基线力
余能原理
有限元
LAGRANGE乘子法
geometrically nonlinear, base line forces, complementary energy, finite element, Lagrange multiplier method
