IMPROVED POTENTIAL ENERGY FORMULATION FOR GEOMETRICALLY NONLINEAR/ POST-BUCKLING ANALYSIS OF FLEXIBLE BEAM STRUCTURES

A novel potential energy approach accounting for the finite displacement effects of beam members have been put forward to address the following issues resulting from applying the well-recognized energy method under the framework of Updated-Lagrangian formulation, which primarily refer to 1) the artificial nodal forces caused by the approximate displacement field model, 2) the theoretical ambiguity regarding the treatment of joint equilibrium during spatial rotations, and 3) the lack of rational physical interpretations about some high order components of total potential energy may pose difficulties as whether they can be ruled out to simplify formulation. Based on the well-known polar decomposition theorem, the potential energy of member forces absorbed during a typical incremental step can be subdivided into three parts, potential energy due to initial member forces developed in the rigid body motion, potential energy caused by natural deformations of the member, and the strain energy, respectively. Using the derived potential energy, the geometric stiffness matrix of a solid spatial beam element that satisfies the rigid body motion test and joint equilibrium requirement in the deformed configuration have been obtained. In this regard, an explicitly formulated incremental secant stiffness matrix has been established to describe member large displacement behavior. Numerical studies revealed that the proposed energy method is capable of reliably tracing nonlinear equilibrium path with a clear physical meaning in analyzing general flexible beam structures.