弹性力学的复变量无网格流形方法  

A meshless manifold method with complex variables for elasticity

作　　者：高洪芬[1,2] 程玉民[1] 姜海辉[3] 

机构地区：[1]上海大学,上海200072 [2]济南铁道职业技术学院,济南250104 [3]山东轻工业学院,济南250353

出　　处：《应用力学学报》2010年第1期15-19,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(10871124);上海市教育委员会科研创新项目(09ZZ99);山东省自然基金(Y2006B24)

摘　　要：为克服无网格流形方法配点过多、计算速度慢、容易形成病态方程组等缺点,将复变量移动最小二乘法与无网格流形方法相结合,提出了弹性力学的复变量无网格流形方法。分别采用线性基本与二次基进行计算,并与无网格流形方法相比。研究表明该方法计算量小、精度高。The pre-processing of the meshless numerical manifold method (MNMM) is simple, but the method concerns dealing with a great many of nodes, is of low computational efficiency and may sometimes lead to an ill-conditioned or singular equations. In this paper, on the basis of complex variable moving least-square approaximation and the MNMM, the complex variable meshless manifold method (CVMNMM) for 2D elasticity is presented, and the corresponding formulae of the CVMNMM are obtained. Compared with the conventional MNMM, the CVMNMM is of high precision and of computational efficiency.

关 键 词：无网格方法 数值流形方法 复变量移动最小二乘法 无网格流形方法 弹性力学 

分 类 号：O343.2[理学—固体力学]