用非协调边界元处理角点问题  

Treatment of Corners Using Discontinuous Boundary Element

作　　者：宋立峰[1] 聂国华[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2009年第3期371-377,共7页Chinese Quarterly of Mechanics

摘　　要：采用非协调单元,有效地解决了边界元的角点问题,给出了含有两个配位因子时非协调线性单元的系数矩阵的表达式,对弹性力学平面问题进行了数值计算。通过采用常数单元、线性非协调单元的计算结果与解析解的比较和分析,证明在均布载荷作用下,两者的计算结果都接近解析解;在非均布载荷作用下,线性单元的结果明显优于常数单元。结果表明,非协调边界元法是一种有效的处理角点问题的方法;线性非协调单元能够更好地处理非均布载荷,提高边界元法的计算精度。Discontinuous boundary element method （BEM） is an approach for treating corner problems in BEM. The expressions were derived for accurate evaluation with two collocation factors of singular integrals, and the numerical implementation of plane elasticity problem is employed. By comparison and analysis the results by discontinuous linear element and by constant element with the analytical solution, both of them are closed to the analytical solution while under uniform load, and the former is more closed to the analytical solution than the latter while under non-uniform load. The results indicate that the discontinu- ous boundary element method is an available method for solving corner problem, and it is more efficiency that analysis plane elasticity problem under non-uniform load by discontinuous linear element than by constant element.

关 键 词：边界元法 线性非协调单元 角点问题 弹性力学平面问题 

分 类 号：O343.1[理学—固体力学]