| Shell structures have been extensively used in civil aerospace, nuclear, marine, and petrochemical industries. In many practical applications, there are instances that there is an opening in a shell. For instance, chimney extend through a shell roof, and manholes break the continuity of a closed vessel. Finding the influence on the membrane stress resultants in the vicinity of an opening is the objective of this dissertation.;The superposition principle is utilized in this investigation. First, by using an ordinary analysis, the membrane stress resultants of the shell without the opening due to the external loading can be obtained. Next consider the equal but opposite stress resultants obtained above as the only applied loads along the edge of the opening, the membrane stress resultants in the vicinity of the opening are then obtained. Finally, by superimposing the two stress resultants together, the membrane stress resultants of the shell with the opening due to the external loads are produced.;In this dissertation, a systematic procedure to find the membrane stresses in the vicinity of the opening due to edge loads is presented. The opening considered has an elliptic horizontal projection. The equilibrium equations and the edge loads constitute an initial-value problem. It is solved by the finite difference method. A spherical storage tank with an elliptic opening subject to a uniform internal pressure is thoroughly studied. The elliptic-hyperbolic coordinate system is used as the reference coordinates of the case study above. A computer program is written to do the numerical computations.;An alternative approach to solve this problem by using the Pucher's stress function is also discussed. The derivation of the Pucher's stress function for the elliptic-hyperbolic coordinate system is then presented. The key points of the Pucher's stress function are: (a) the three membrane stress resultants are derived from the function; (b) next the two equilibrium equations for forces in the shell surface are satisfied identically; (c) and finally the stress function is then obtained from the third equilibrium equation in the direction normal to the shell surface. Therefore the use of the Pucher's stress function replaces the three unknown membrane stress resultants by only one unknown--Pucher's stress function. Pucher introduced his stress function in the planar horizontal Cartesian coordinates. Langhaar extended it in the horizontal polar coordinates. In this dissertation, a further extension to the formulation in the planar elliptical-hyperbolic coordinates is made. |
