Abstract: The study of bending of cracked circular cylinders is of more significance. The bending of cylinders containing radical crack or cracks was discussed by refs. [1]-[4] and that of concentrically craked circular cylinders was studied by [5]. Continuing [6] and using complex variable methods in elasticity, this paper deals with the bending problems of a circular cylinder, containing an internal linear crack at any position under an acting force perpendicular to the crack. The general forms of displacements, stresses, and stress-intensity factors, expressed in terms of series, are obtained and to this bending problems with small Ah are presented good approximate formulas for the stress-intensity factors whose variations with the center of the crack are analysed. Finally, the twist angle per unit length and the center of bending for the radically cracked circular cylinder, one of whose crack-tips is located at the origin, have been computed and the results are almost the same as that calculated in [1].

Key words: two-level method, Navier-Stokes equation, residual a posteriori error estimate, finite element method, stream function form