Improved nonlinear finite elements for oriented bodies using an extension of marguerre's theory

Abstract A simple method to develop improved finite elements for the analysis of materially and geometrically nonlinear oriented bodies (beams, plates) is presented. It is based on an approximate updated Lagrangian description of the motion, that uses a straight reference configuration affected by initial deflections to take account of the curvature of the actual structure. These deflections are introduced in the model via an extension of Marguerre's theory. Examples with two-and-three dimensional beam and plate-membrane elements illustrate the effectiveness of the method.