Automatic Solution of Pucher's Equation

The system of shell membrane force-equilibrium equations expressed in terms of cartesian coordinates can be reduced to a single differential equation, called Pucher's equation, involving a stress function and the coordinate defining the elevation of the shell surface. A computer program which completely automates the solution of Pucher's equation is described. This program is restricted to the case where the loading is vertical and the projected shell boundary consists of straight line segments. Collatz's method is used to establish a system of difference equations. Results for an elliptic paraboloid of square plan and a paraboloid of revolution having a triangular boundary are compared with the exact solutions and show excellent agreement.