Large Deflected Plates and Shells with Loading History

Abstract

Among the problems in the design of geometrically nonlinear plates and shells, there is a special class in which the total stress‐strain behavior must be considered with loading history. The loading history includes the plate‐shell loading, boundary conditions, and material behavior, but assumes only the “discrete steps” in the aforementioned considerations. To indicate the difference between “discrete steps,” the axisymmetrical bending of plates and shells is presented along with suitable differential equations for loading history. The supplemental terms are derived and the results illustrated with numerical examples. The arbitrarily loaded large deformed plates and shallow shells are presented along with suitable differential equations for discrete loading history. The importance of variable curvature versus constant curvature consideration is shown for large deformed shallow shells. With consideration of geometrical and statical heredity of every two successive steps of loading history, the linearization can simplify calculations of plates and shells with large deflections.