Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex var...Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles.展开更多
文摘Based on Donnell's shallow shell equation, a new method is given in this paper to analyze theoretical solutions of stress concentrations about cylindrical shells with large openings. With the method of complex variable function, a series' of conformal mapping functions are obtained from different cutouts' boundary curves in the developed plane of a cylindrical shell to the unit circle. And, the general expressions for the equations of a cylindrical shell, including the solutions of stress concentrations meeting the boundary conditions of the large openings' edges, are given in the mapping plane. Furthermore, by applying the orthogonal function expansion technique, the problem can be summarized into the solution of infinite algebraic equation series. Finally, numerical results are obtained for stress concentration factors at the cutout's edge with various opening's ratios and different loading conditions. This new method, at the same time, gives a possibility to the research of cylindrical shells with large non-circular openings or with nozzles.
