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

作　　者：温伟斌 蹇开林 骆少明 

机构地区：[1]School of Resources and Environmental Science, Chongqing University [2]State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University [3]Faculty of Mechanical and Electrical Engineering, Zhongkai University of Agriculture and Engineering

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第8期1017-1030,共14页应用数学和力学（英文版）

基　　金：supported by the Fund of National Engineering and Research Center for Highways in Mountain Area(No.gsgzj-2012-05);the Fundamental Research Funds for the Central Universities of China(No.CDJXS12240003);the Scientific Research Foundation of State Key Laboratory of Coal Mine Disaster Dynamics and Control(No.2011DA105287-MS201213)

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 conven- tional 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 prin- ciple 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.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 conven- tional 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 prin- ciple 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：numerical manifold method （NMM） manifold element B-SPLINE thinplate bending 

分 类 号：O174.42[理学—数学]