tailieunhanh - Applied Structural Mechanics Fundamentals of Elasticity Part 9

Tham khảo tài liệu 'applied structural mechanics fundamentals of elasticity part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 226 13 Bending theory of shells of revolution Solution for a cylindrical shell with semi-infinite length subjected to boundary loads M R see Fig. w 2 a 2k2K 2k a R cos K M cos K - sin K e A. e . __lĩ Í R sin K M cos fí. sin K e f . 2 K _ _ . R cos k. - sin K - -7- M sin K e l a 2 Spherical shell - Method by GECKELER This method utilizes the fast decay of boundary disturbances in a circular cylindrical shell x e- . The essential MEISSNER equations are the starting relations for the approximation method . The following two uncoupled differential equations for the bending angle X and the transverse force are obtained d dọp v 0 with Q __ t 4 - 0 4 Eta2 K 2 - V V2 can be neglected in the case of thin-walled shells Y 1. Then the decay factor given by can be used. 3 Circular conical shell - Method by GECKELER In this case it is also assumed that a fast decay of the disturbances from the boundaries occurs. The corresponding differential equation reads d ds s Q. ft 2 with Kj 3 1 - s t Basic equations for arbitrary loads 227 Fig. Displacements of the boundaries for cylindrical and spherical shells in dependence on the boundary loads R and M Here the decay factor depends on the variable s . Owing to the limitation to narrow boundary zones r2 S8 const we can assume the decay factor to be approximately constant in these areas. Thus we obtain the same solution as when considering spherical shells. Fig. Substitute of a conical shell by spherical shells at the boundaries 220 13 Bending theory of shells of revolution 4 Combined shell structures - Solution by Method of Theory of Structures The force-quantity procedure the so-called Method of Theory of Structures for the analytical layout of combined structures can also be used successfully in shell statics. After a partitioning into single substructures 0 1 2 -System etc. compatibility conditions have to be formulated at the