UNIQUENESS OF SOLUTION OF FIELD POINT OF SINGULAR SOURCE OUTSIDE-REGION-DISTRIBUTION METHOD

摘要/Abstract

摘要： The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outsidergeion-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality. Examples of part ofthese singular sources such as Kelvin’s point force, Point-Ring-Couple (PRC) etc.are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.

关键词: solution of singular sources, singular source outside-region-distribution Method, non-singular integral equation method, boundary element Method, line-loaded integral equation method

Abstract: The uniqueness of solution of field point, inside a convex region due to singular source(s) with kernel function decreasing with distance increasing, outsidergeion-distribution(s) such that the boundary condition expressed by the response of the source(s) is satisfied, is proved by using the condition of kernel function decreasing with distance increasing and an integral inequality. Examples of part ofthese singular sources such as Kelvin’s point force, Point-Ring-Couple (PRC) etc.are given. The proof of uniqueness of solution of field point in a twisted shaft of revolution due to PRC distribution is given as an example of application.

Key words: solution of singular sources, singular source outside-region-distribution Method, non-singular integral equation method, boundary element Method, line-loaded integral equation method

云天铨. UNIQUENESS OF SOLUTION OF FIELD POINT OF SINGULAR SOURCE OUTSIDE-REGION-DISTRIBUTION METHOD[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(1): 36-42.

Yun Tianquan. UNIQUENESS OF SOLUTION OF FIELD POINT OF SINGULAR SOURCE OUTSIDE-REGION-DISTRIBUTION METHOD[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(1): 36-42.

参考文献

[1] Yun Tianquan. Integral Equations and Its Applications in Mechanics [M]. Guangzhou:South China University of Technology PUblishers, 1990. 324～327 (in Chinese)
[2] Yun Tianquan. An integral equation method for solving the torsion problem of revolution bodies [J]. Journal of Hua-Zhong Institute of Technology (English Edition), 1979, 1 (1): 82～98
[3] Yun Tianquan. Pile analysis by simple inteqrul equation methods [J]. Applied Mathematics and Mechanics, 1981,2 (3): 331～3480
[4] Wu B C, Altiero N J. A new numerical method for the analysis of anisotropic thin-platebending problems[J]. Computer Methods in Appl Mech Eng, 1981, (25): 343～353
[5] Yun Tianquan, Shao U C, Qiu C Q. Analysis of ellipsoed compressed by two axial concentrated forces at two ends [J]. Applied Mathematics and Mechanics, 1981,2 (6): 699～710
[6] Yun Tianquan. An integral equation method for solving the problem of elastic layer on horizontal rigid base subjected to perpendicular concentrated force, Acta Mechanics SolidaSinica, 1983, (3): 375～382 (in Chinese)
[7] Yun Tianquan. Line-loaded integral equation method for the analysis of axially loaded rigidpile embedded in a sloping elastic half space [J]. Acta Mechanics Solida Sinica, 1986, (3):64～68 (in Chinese)
[8] Yun Tianquan, Zhang J M. Analysis of shaft by line-loaded integral equation method [J]. Shanghai Mechanics, 1986, 7 (1): 50～54 (Chinese)
[9] Yun Tianquan. Torsion of rigid circular shaft of varying diameter embedded in an elastichalf space[J]. Applied Mathematics and Mechanics, 1988,9 (5): 449～453
[10] Yun Tianquan.Torsion of elastic shaft of revolution embedded in an elastic half space[J]. Applied Mathematics and Mechanics, 1990,11 (6): 489～498
[11] Yun Tianquan.Analysis of sloping rigid pile under arbitrary load by line-loaded integral equation method [A]. In: eds Cheung, Lee Leung. Computational Mechanics Proc of APCOM, Vol. 1 [C], Hong Kong: Balkema, Rotterdam, 1991,845～850
[12] Yun Tianquan,Su C. Analysis of shaft embedded in granular half space by the line-loaded integral equation method [J]. COmputers & Structures, 1992, 43 (4): 729～735
[13] Yun Tianquan,Gu H N. The solution of dynamic POint-ring-couple in an elastic spaceand its properties [J]. Applied Mathematics and Mechanics, 1993, 14(10): 845～852
[14] Yun Tianquan. Analysis of strUcture system based on in-plane-hinge-jointed rigid slopingpiles group by line-loaded integral equation method[A]. Theory and APPlications of Reaction between Structures and media [M]. Zhao Zhiyuan ed. Naming: University of caver & Sea PUblishers, 1993. 632～635(in Chinese)
[15] Yun Tianquan,Li L H. Analysis of in-plane-hinge-jointed rigid sloping piles[J]. Computers & Structures, 1995, 55(2): 341～346
[16] Yun Tianquan. Elastodynamic analysis of torsion of shaft of revolution by line-loaded integral equation method [J]. Structural Engineering and Mechanics, 1998, 6 (3)
[17] Yun Tianquan,Gu H N. Analysis of axially loaded pile in linear viscoelastic half space[J]. Journal of South China University of Technology, 1995, 23(4): 47～52(in Chinese)
[18] Yun Tianquan. Uniqueness theorem of nonsingular integral equation method [J]. Tran sactions CSME, 1986, 10(4): 197～200
[19] Brebbia C. A.Progress in Boundary Element Methods [M], Vol. 1 London: PentechPress, 1981, 171.