Geometrically nonlinear finite element analysis of functionally graded 3D beams considering warping effects

Abstract

We present a geometrically nonlinear finite element formulation for analysis of functionally graded 3D beams. The proposed formulation employs the continuum mechanics based beam element with the warping displacement to model complex modes of deformation. The novelty of the developed method is that the warping function can be accurately calculated for any beam with arbitrary cross-sections and material grading patterns. Superb performances of the proposed beam element are demonstrated through several representative examples.