正交各向异性弹性力学平面问题的样条虚边界元法

苏成; 韩大建

正交各向异性弹性力学平面问题的样条虚边界元法

苏成,
韩大建

华南理工大学, 土木工程系, 广州, 510640

基金项目: 广东省自然科学基金资助项目(984059)

详细信息

作者简介:
苏成(1968- ),男,广东潮阳人,副教授,博士,已发表论文30余篇,主要研究方向:计算力学、高层建筑结构、桥梁结构.

中图分类号: O343.8
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- 被引次数: 0
出版历程
- 收稿日期: 2000-11-20
- 修回日期: 2001-10-09
- 刊出日期: 2002-04-15

Elastic Analysis of Orthotropic Plane Problems by the Spline Fictitious Boundary Element Method

Department of Civil Engineering, South China University of Technology, Guangzhou 510640, P. R. China

摘要

摘要: 采用域外奇点技术并根据问题的边界条件,建立了正交各向异性弹性力学平面问题的非奇异虚边界积分方程,然后采用性态优越的B样条函数去逼近未知虚荷载函数,并采用性能稳定的最小二乘边界子段法去消除边界余量,据此获得积分方程的数值解.数值算例表明:该方法具有相当高的精度和良好的数值稳定性,且计算工作量少.文中引言部分还对域外奇点法的发展作了系统的评述.
- 正交各向异性 /
- 平面问题 /
- 样条函数 /
- 边界元法
Abstract: Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.
- orthotropic /
- plane problem /
- spline function /
- boundary element method

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参考文献(33)

[1]	Banerjee P K,Butterfield R.Boundary Element Method in Engineering Science[M].London:McGraw-Hill,1981.
[2]	姚振汉,钟晓光.边界元法中边界变量的确定与误差直观度量[J].华中理工大学学报,1989,17(6):91-103.
[3]	王元丰,邹永超.边界元边界层处理的一种新方法--拟多连域法[J].应用力学学报,1997,14(1):124-127.
[4]	马杭.边界变换法求边界近傍的应力[J].力学与实践,1990,12(3):39-40.
[5]	Patterson C,Sheikh M A.Regular boundary integral equation for stress analysis[A].In:Brebbia C A Ed.Boundary Element Methods[C].Berlin:Springer-Verlag,1981,85-104.
[6]	Patterson C,Sheikh M A.A regular boundary element method for fluid flow[J].Int J Num Methods in Fluids,1982,(2).
[7]	许永林,唐锦春.域外奇点法及格林函数公式法解析弯曲问题[J].计算结构力学及其应用,1986,3(2):9-17.
[8]	孙炳楠,唐锦春,项玉寅.平板弯曲边界元域外奇点新方法[J].计算结构力学及其应用,1991,8(1):101-107.
[9]	卢习林,林庆华.无奇性边界元法解平板弯曲问题[J].清华大学学报,1988,28(2):12-27.
[10]	刘维倩.弹性力学的正则边界积分方程-边界元法及其应用软件[A].见:李家宝主编.全国第一届解析与数值结合法会议论文集[C].长沙:湖南大学出版社,1989,294-300.
[11]	傅铱铭.用域外配点边界元法求解二维平面内波动问题[A].见:李家宝主编.全国第一届解析与数值结合法会议论文集[C].长沙:湖南大学出版社,1989,328-331.
[12]	YUN Tian-quan.An integral equation method for solving the torsion problem of revolution bodies[J].Journal of Huazhong Institute of Technology,1979,1(1):82-97.
[13]	云天铨.简便积分方程法分析桩[J].应用数学和力学,1981,2(3):307-320.
[14]	苏成.线荷载积分方程法分析嵌于粒状半空间的竖桩[J].华南理工大学学报,1993,21(1):18-24.
[15]	YUN Tian-quan,SU Cheng.Analysis of a shaft embedded in granular half space by the line-loaded integral equation method[J].Computers & Structures,1992,43(4):729-735.
[16]	李丹.板弯曲问题的边界元解法[A].见:第三届全国建工系统计算机应用学术交流会论文集(2)[C].海口,1986,480-491.
[17]	孙焕纯,李性厚,张立洲.弹性力学问题的虚边界元-配点法[J].计算结构力学及其应用,1991,8(1):15-23.
[18]	Wu B C,Altiero N J.A new numerical method for the analysis of anisotropic thin-plate bending problems[J].Computer Methods in Applied Mechanics and Engineering,1981,(25):343-353.
[19]	Redekop D,Thompson J C.Use of fundamental solutions in the collocation method in axisymmetric elastostatics[J].Computers & Structures,1983,17(4):485-490.
[20]	金梦石.应用嵌入法分析板的弯曲问题[J].应用力学学报,1986,3(3):93-103.
[21]	金梦石.应用Green函数法计算平面弹性力学问题[J].应用力学学报,1988,5(2):17-26.
[22]	苏成,韩大建.域外奇点法分析薄板的弯曲和平面应力问题[J].工程力学,1994,11(4):17-26.
[23]	苏成,韩大建.域外奇点法分析折板结构[J].力学与实践,1995,17(1):24-27.
[24]	苏成,韩大建.非均匀弹性支承Reissner板分析的域外奇点法[J].力学与实践,1997,19(5):34-36.
[25]	王元淳,Sekiya T.域外奇点法在弹性问题及其物性值反问题中的应用[J].上海力学,1994,15(2):84-90.
[26]	Tomlin G R,Butterfield R.Elastic analysis of zoned orthotropic continua[J].Proc ASCE,1974,100(EM3):511-529.
[27]	秦荣.结构力学的样条函数方法[M].南宁:广西人民出版社,1985,9-16.
[28]	苏成,韩大建.弹性力学平面问题的虚边界元-边界子段法[J].华南理工大学学报,1998,26(3):22-26.
[29]	SU Cheng,HAN Da-jian.Multidomain SFBEM and its application in elastic plane problems[J].Journal of Engineering Mechanics,ASCE,2000,126(10):1057-1063.
[30]	徐次达.固体力学加权残值法[M].上海:同济大学出版社,1987,41-44.
[31]	吴兹潜,张佑启,范寿昌.结构分析的样条有限条法[M].广州:广东科技出版社,1986,91-92.
[32]	苏成,韩大建.高层建筑侧向刚度计算的分域样条虚边界元法[J].华南理工大学学报,1998,26(6):81-85.
[33]	苏成,韩大建.高层建筑筏板基础分析的样条虚边界元法[J].土木工程学报,2001,34(1):61-66.