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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (8): 1017-1030.doi: https://doi.org/10.1007/s10483-013-1724-x

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2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

温伟斌1 蹇开林1,2 骆少明3   

  1. 1. School of Resources and Environmental Science, Chongqing University, Chongqing 400044, P. R. China;
    2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, P. R. China;
    3. Faculty of Mechanical and Electrical Engineering, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, P. R. China
  • 出版日期:2013-07-15 发布日期:2013-07-15
  • 通讯作者: Kai-lin JIAN E-mail:cqjian@cqu.deu.cn

2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

Wei-bin WEN1, Kai-lin JIAN1,2, Shao-ming LUO3   

  1. 1. School of Resources and Environmental Science, Chongqing University, Chongqing 400044, P. R. China;
    2. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044, P. R. China;
    3. Faculty of Mechanical and Electrical Engineering, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, P. R. China
  • Online:2013-07-15 Published:2013-07-15
  • Contact: Kai-lin JIAN E-mail:cqjian@cqu.deu.cn

PDF

689

被引次数

18

摘要：

A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conventional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the principle
of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

关键词: manifold element, thin plate bending, numerical manifold method (NMM), B-spline

Abstract:

A new numerical manifold (NMM) method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conventional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the principle
of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

Key words: basic system of equations of atmospheric motion, stability, stratification theory, transversal stratum, numerical manifold method (NMM), thin plate bending, manifold element, B-spline

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