Convergence of Hypar Finite-Difference Solutions

A study of the convergence rates of finite-difference solutions of the linear thin shallow shell equations for single panel ruled surface hyperbolic paraboloids is reported. Boundary conditions of clamped, simply supported edges, free edges and edges elastically supported on edge beams are shown to have a considerable effect on the convergence rates. Using conventional finite-difference methods and an iterative method of solution, investigations with successively finer grids show that satisfactory convergence of in-plane actions is obtained on relatively coarse difference grids (grid spacings less than 8 in both directions over 1/4 of the shell area), and that convergence of moments and deflections require finer grids. Higher order boundary approximations and the modified finite-difference technique give slightly increased accuracy only at the expense of greatly increased computational effort.