Numerical Analysis of Translational Shell Roofs

A method is presented for the computer analysis of translational shells by numerical integration. Both the general cylindrical shell equations, obtained from Love and Reissner, and a simplified set of equations for shallow translational shells are formulated for numerical integration. A Lévy type solution is assumed for the shell displacements and the governing partial differential equations are reduced to a system of eight first order linear differential equations. The shell boundary value problem is converted into an initial value problem that is solved on a digital computer by a numerical integration scheme permitting the rigorous analysis of a translational shell with variable thickness, curvature, and loading. The number of simultaneous equations to be solved depends only on the number of boundary conditions and not on the number of integration steps. Numerical examples are given to illustrate the behavior of cylindrical shells with both variable thickness and variable curvature and doubly curved translational shells. Numerical results are examined in terms of accuracy and computer time.