Efficient calculation method for dynamic behaviour and seismic performance of reciprocal structures based on condensed nodal coding system

This paper proposes an efficient method for calculating the dynamic behaviour and seismic performance of reciprocal structures by introducing the generalized displacements at the hinge point to describe the displacements of the nodes at the beam ends. The whole structural nodal coding system is condensed by replacing the two codes at the beam end nodes with code at the hinge point based on the traditional space rigid frame matrix displacement method. On the basis of the principle of virtual work, the system natural vibration equation of the structure in the condensed nodal coding system is obtained; from the mode-superposition response spectrum method and the time history analysis method, the system seismic response equation of the structure in the condensed nodal coding system is derived. Then, the dynamic behaviour and seismic performance of the structure can be achieved by solving the obtained system dynamic equations. Finally, two numerical examples, a space L-shaped articulated reciprocal rigid frame and a reciprocal configuration transformed from the 36 type of Archimedes paving, are adopted to demonstrate the effectiveness of the proposed method. From the numerical results, the reciprocal structure transformed from the 36 type of Archimedes paving has a large whole stiffness, and the seismic response generated by vertical earthquake excitation is the most significant, which should be the focus of the seismic design of reciprocal structures. The proposed method effectively reduces the number of computational degrees of freedom of the whole structure and is more efficient in calculating the reciprocal structure.