Multi-scale Finite Element Method for Members for Pipe Frames

To consider the local buckling of the members in reticulated frames, based on the multi-scale simulation, the part of member may be collapsed were divided by the shell elements as a micro-model, and the other part of the member was simulated by beam elements as a macro-model. The incremental displacement constraint equations for the nodes on the section between the two models are established based on the plane section premise of classical beam theory. By constraint variational principle, the tangent stiffness matrixes and the nodal load vectors of the micro-model and the outside structure are combined, and then the equations are solved. The location of the collapsed part is predicted by the deflection function of the beam, and the length of the collapsed part is estimated. Two case studies about a single beam and a single-layer reticulated dome are presented to show the feasibility and the validity of this method.