Consider the cut-and-weld problem in which a small wedge of angle a is removed from an annular ring as shown in the figure. The ring is then to be joined back together (welded) at the cut section. This operation produces an axisymmetric stress field, but the problem will contain a cyclic tangential displacement condition u_θ (r,2π) –u_θ (r,0) = αr. First using the general plane stress solution (8.3.9)₂, drop the rigid-body motion terms and show that the constant a₃ is given by:

Equation 8.3.9

Transcribed Image Text:

Ur ug = (1 v) 1/2 [ _- ( + ") a r -a + 2(1 v)a3r log r- (1+v)a3r+2a2(1 + A sin + B cose 4r0 E a3 + A cose B sin + Cr 2a2(1 - v)r] - (8.3.9)