Applied Mathematics and Mechanics (English Edition) ›› 1993, Vol. 14 ›› Issue (12): 1143-1150.

• 论文 • 上一篇    下一篇

ON THE MATHEMATICAL PROBLEMS OF COMPOSITE MATERIALS WITH A DOUBLY PERIODIC SET OF CRACKS

李星   

  1. Ningxia University, Yinchuan
  • 收稿日期:1992-07-24 出版日期:1993-12-18 发布日期:1993-12-18
  • 基金资助:
    Project supported by the National Natural Science Foundation of China

ON THE MATHEMATICAL PROBLEMS OF COMPOSITE MATERIALS WITH A DOUBLY PERIODIC SET OF CRACKS

Li Xing   

  1. Ningxia University, Yinchuan
  • Received:1992-07-24 Online:1993-12-18 Published:1993-12-18
  • Supported by:
    Project supported by the National Natural Science Foundation of China

摘要: In this paper, the mathematical problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated, and the interface are arbitrary smooth closed contours. At first, we establish mathematical models by using Muskhelisvili complex variable methods, change the primitive problems into searching complex stress functions which satisfy four boundary value problems and construct forms of the solution, then, under some general restrictions it is reduced to normal type singular integral equation, the unique solvability is proved mathematically.

Abstract: In this paper, the mathematical problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated, and the interface are arbitrary smooth closed contours. At first, we establish mathematical models by using Muskhelisvili complex variable methods, change the primitive problems into searching complex stress functions which satisfy four boundary value problems and construct forms of the solution, then, under some general restrictions it is reduced to normal type singular integral equation, the unique solvability is proved mathematically.

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