The Lumped-Parameter or Bar–Node Model Approach to Thin-Shell Analysis

Abstract

The bar-node or lumped-parameter model represents an analog to the finite-difference equations. As the model is developed based on physical concepts, it yields a system of equations that are consistent—that is, whether the equilibrium equations or the variational method is used, the procedure yields the same equations. The development of the governing equations for the lumped-parameter model will be illustrated for the particular case of an elastic isotropic shallow shell. However, the analog model concept is equally applicable to other shell theories and produces results of superior accuracy for these as well. The modification of strain-displacement relations is necessary whether or not explicit consideration is to be given to stress boundary conditions. The membrane strain-displacement relations are modified only for nodes lying on the boundary. The necessary modifications to the bending strain-displacement relations are more complicated when the stress boundary conditions are to be satisfied exactly. In order to account properly for the transfer of the twisting moment to the rigid bar intersection in the case of a free edge, auxiliary rigid bars are introduced into the physical mode.