摘要
将数值流形方法应用于薄板弯曲变形的分析,采用标准矩形网格作为数学网格,并提出16节点的矩形薄板流形单元,推导出用于薄板弯曲分析的流形格式和单元矩阵;单元节点的覆盖函数采用C0和C1阶的局部多项式函数形式,单元采用覆盖自由度为基本求解变量,解决了有限元法中采用挠度和转角为求解变量的复杂计算过程;该16节点流形单元应用于正方形薄板弯曲变形的实例分析,结果表明,与有限元分析相比,流形单元的计算精度和收敛性可大幅度提高。
Numerical manifold method is applied to analyze thin plate bending deformation. 16-node manifold element is constructed based on cover system with rectangular mathematical mesh. Numerical manifold formulas and element matrices are derived in this paper. C^0 and C^1 local polynomial is adopted as the node cover function, cover DOF is defined as the basic unknown variables, and it can overcome the very complicated computation process in FEM with deflection and rotational angle as the unknown variables. As an application, 16-node manifold element is used to analyze bending deformation of square thin plate; the results show that numerical manifold method with 16-node element, compared with finite element method, can improve accuracy and convergence greatly.
出处
《塑性工程学报》
CAS
CSCD
北大核心
2009年第4期29-34,共6页
Journal of Plasticity Engineering
基金
国家自然科学基金资助项目(50775044)
教育部博士点基金资助项目(20050562003)
关键词
薄板弯曲
数值流形
流形单元
thin plate bending
numerical manifold method
manifold element
