The general solutions of an infinite plate with doubly periodic cracks under bending and twisting

✍ Scribed by S.S. Chang

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 458 KB
• Volume: 20
• Category: Article
• ISSN: 0013-7944
• DOI: 10.1016/0013-7944(84)90060-2

✦ Synopsis

objective of the present paper is to use the basic theorem of Jacobi elliptic functions and residues to find the general solutions of the stress intensity factor of a plate with doubly periodic cracks subjected to a pair of concentrated couples Mb and M, on the faces of each crack.

In this paper the general solutions are expressed in simply closed forms, and they can also be applied to solve practical problems of bending and torsion of a rectangular sheet containing a central crack. The general solutions may be used as a fundamental Green's fimction for tinding other solutions of a plate with doubly periodic cracks under arbitrary bending and twisting moments. It is easily proved that all problems of bending and torsion of an intinite plate with a central crack or singly periodic cracks, are the special cases of the general solutions in this paper.

FUNDAMENTAL EQUATIONS AND RELATIONS

FOR CONVENIENCE, we will only find the complex stress-function? for determining the stress intensity factor of bending and torsion of a cracked-plate because it is the key problem in this paper.

The maximum values of the stress intensity factors K, and K,, occurring at the surface layer of a