Stresses and Displacements of a Shallow Spherical Shell under an Eccentrically Applied Concentrated Load

摘要

This paper is concerned with the stresses and displacements in a shallow spherical shell subjected to an arbitrarily located concentrated normal force. A shallow shell, clamped at the outer boundary, and having a circular polar aperture, free of tractions and support, is examined in detail. The freedom to locate the concentrated load arbitrarily permits the examination of the influence of the boundary effects on the resulting stress distribution. These effects and the general character of the stress field are central areas of the investigation. Numerical results, obtained on a digital computer, are presented graphically for a typical shell with and without a central opening, for three locations of the concentrated load. In general, the effects of the opening causes significant deviations of the stress pattern in the neighborhood of the boundary. However, when the load is applied at some distance from the aperture the principal stresses in the shell occur in the neighborhood of the singular load rather than at the aperture. When the load is applied near the outer boundary, the moment resultants are unaffected at the opening, but undergo a sharp increase near that edge. (Author)