Tham khảo tài liệu 'applied structural mechanics fundamentals of elasticity part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 286 13 Bending theory of shells of revolution constants The complex constants Aj Bj Cj j 1 2 are coupled to each other via a homogeneous system of equations. The first equation for m 1 k 1 yields h - j-bi T-Mj ihcJ 0 -Fm CJ 0 and for j 1 with Xj - Pj i Pi we obtain the following dependencies of the - 1 2 V Hj 4 i 1 2 V 1J 1 c ot i a2 c Ợ 1 i 2 c pi ip2 C1 . Since X2 - Uj - Ì Pj the conjugate complex relations for j 2 follow as A2 1-i 2 c2 B2 pj- ip2 c2 . 8 M 1 If we substitute 7 and 8 into 6 all displacements depend on Cj and C2 only. Boundary conditions If we consider the boundary Ẹ 0 only in the case of the membrane solution the two boundary conditions for Ẹ 0 and Ệ a have to be replaced by two symmetry conditions for E 112a. We thus obtain from N Ấấ C und U 2i 0 with lb and 3a The remaining four constants Ci c2 D2 conditions and D4 result from the four boundary u o u 0 - 0 v o v 0 V1 0 0 w o WD 0 w1 0 0 w 0 . After carrying out the numerical calculation with the given values we obtain the circumferential force as Nứú N - 8 cos sin e 12-9 cos s . Exercise C-13-4 2B7 Fig. C-25 shows the membrane forces according to 1 and the bending moments Mxx und acting along the top longitudinal line 3 0 of the shell. One can see how fast the bending disturbance has decayed already at a distance of m from the boundary. The stresses are calculated from Fig. C-25 Membrane forces and bending moments along the top longitudinal line of the cylindrical tube under deadweight 2B8 13 Bending theory of shells of revolution The maximum stresses at the boundary are due to 9 ốvv 4-x MPa. 0. 0-39 0 28 MPa . The numerical values show that both the longitudinal and the circumferential stresses due to the boundary disturbances are of similar magnitude as the membrane stresses. Exercise C-13-5 A circular cylindrical shell fa Ỉ 4a t a 400 is subjected to a constant external pressure p Fig. C-26 . Formulate the basic equation for shell buckling ill .
