摘要
在有限元三维20结点单元构成的空间网格上构建流形覆盖和权函数,采用拉格朗日乘子法施加位移约束条件,推导了分析静态问题的计算列式。无需细致网格划分即可更精确地分析具有曲线边界的区域,计算结果的误差能量模较有限元法降低超过一个量级。对采用完全1阶覆盖函数时的线性相关性进行了分析,提出在单元角结点上采用1阶覆盖函数基,其他结点上采用零阶覆盖函数基的方法。利用算例分析了用这种方法计算的两套覆盖函数的收敛率。数值算例表明:效果明显,对解答有体积闭锁的问题均有很高精度。
The numerical manifold method (NMM) has been widely used for 2D problems. The construction of numerical manifold covers and weight functions on traditional 3D twenty-node iso-parametric element meshes of FEM is proposed in the paper. With Lagrange multiplier,Dirichlet boundary conditions are imposed along the essential boundaries. Formulae for static analysis are given. Then it is easier to model 3D problems with curved boundary surfaces by using the NMM without fine meshing in common FEM. Linear dependency of the approximation space is studied,and a method of applying enhanced cover functions only at physical covers connected to corner vertices is proposed to resolve this problem. Thus the scale of discrete system decreases more significantly than that in conventional implementations of the NMM. Example analyses show that the error energy norms decrease dramatically to about ten percent of the corresponding FEM results both in common and volume-locking cases. Convergence rates are also studied with examples and they are approximately equal in the NMM and the conventional FEM analyses for both material cases. The compatibility of the conventional FEM procedure with the 3D NMM analytical procedure is considered from the scratch of its design,which ensures a smooth and easy interface for developing an NMM analytical system from the existing FEM procedures.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2004年第15期2622-2627,共6页
Chinese Journal of Rock Mechanics and Engineering
关键词
数值分析
数值流形方法
拉格朗日乘子法
20结点单元
体积闭锁
numerical analysis,numerical manifold method,Lagrange multiplier,twenty-node iso-parametrical element,volume-lock
