Achsensymmetrische Deformation von Umdrehungskörpern

Analysis of residual stresses in a long hollow cylinder

“…(28) takes the following form: The remaining constants of integration A and B in Eqs. (33) and (34) can be found from the boundary conditions (31) and (32) s r ¼ A 2r 2 ð1 þ nÞ r 2 I 0 ðsrÞ þ r s 2n À 2 À s 2 r 2 I 1 ðsrÞ À k s 2n À 2 À s 2 k 2 I 1 ðskÞ þ q 1 ðrÞI 0 ðsÞ À q 2 ðrÞI 0 ðskÞ ! þ B 2r 2 ð1 þ nÞ After all the stress-tensor components are found as the Fourier transforms, the original stresses can be computed by means of the inverse transformation:…”

“…hjðhÞc 00 ðr; hÞdh; (33) where A and B are the constants of integration and c ij ðx; yÞ ¼ I i ðsxÞK j ðsyÞ À ðÀ1Þ iþj K i ðsxÞI j ðsyÞ:…”

“…By making use of Eq. (33) and eliminating the constants of inte-gration from the boundary conditions (30), the solution of Eq. (28) takes the following form: The remaining constants of integration A and B in Eqs.…”

“…Love [32] represented a general solution to the axisymmetric problem in terms of one biharmonic function. Different dominant methods are based on solutions in the form suggested by Weber [33], Timpe [34], Papkovich-Neuber [35,36], and Michell [37]. The solution of the non-axisymmetric problems is more complicated.…”

“…and (34), the expression for axial stress Eq. (22) along with Eqs (33),(34),. and (36), we determine the radial stress in the following form:…”