Complete Plane Strain Problem of a Nonhomogeneous Elastic Body with a Doubly-Periodic Set of Cracks

✍ Scribed by X. Li

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 194 KB
• Volume: 81
• Category: Article
• ISSN: 0044-2267
• DOI: 10.1002/1521-4001(200106)81:6<377::aid-zamm377>3.0.co;2-q

✦ Synopsis

In this paper, we wish to use complex potential methods to solve the fundamental complete plane strain (CPS) problems of a three-dimensional nonhomogeneous elastic body with a doubly-periodic set of cracks in the x 1 , x 2 plane. We resolve the complete plane strain state, which is a special three-dimensional elastic system, into two linearly independent twodimensional (plane) elastic systems by the superposition principle of force. Based on a suitable modification of Cauchytype integrals, which is defined by the replacement of the Cauchy kernel 1=ðt À zÞ by the Weierstrass zeta function zðt À zÞ, the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel, and the existence of an essentially unique solution is proved.