An Indirect Boundary Integral Equation Applied to Nonshallow Spherical Shell Problems With Arbitrary Boundary Constraints

Abstract

The fundamental singular solutions of a complete elastic spherical shell are utilized and, via the superposition principle, an indirect boundary integral equation is formulated. The singular solutions correspond to the action of normal point loads, concentrated tangential loads, and surface moments which apply in a self-equilibrating fashion over the spherical surface. With singular solutions of such property in hand, an arbitrary spherical shell with surface loading and any set of consistent boundary constraints is embedded onto the complete sphere. A set of fictitious load vectors is introduced along the boundary line which, together with the prescribed surface traction, is required to satisfy the constraints at the boundary. The idea of an auxiliary boundary is also introduced and the solution to a number of representative shell problems is shown as compared to the available analytical and finite element method results.