A Variational Approach to Address the Problem of Planar Nonlinear Beams

Various nonlinear planar beam models are presented and discussed using a variational approach. Particular attention is paid to the introduction of the strain energy functional and the determination of suitable strain measures and kinematic descriptors. Shear deformability or non-deformability is emphasized as a qualifier between the different models. Some attention is also given to the case where the beam cross-section is deformable. Problems of dynamics and dissipation are mentioned to complete the discussion.