Novel static calculation approach for reciprocal structures assembled by Archimedes paving curved rods

In order to more efficiently solve the internal forces and deformations of the curved rod reciprocal structures transformed from the Archimedes paving, the reference point is defined on the curved rod element in this paper. On the basic of the static equilibrium relationship between the forces at the reciprocal articulated joints and the generalized nodal loads at the reference point, the static equilibrium equation of the curved rod reciprocal structure is established. By solving the equilibrium equation, the nodal forces of the curved rod reciprocal structure can be obtained. Furthermore, the internal forces and deformations of the reciprocal curved rod in the cylindrical coordinate system are derived by coordinate transformations. Finally, a quadrilateral curved rod reciprocal frame and a curved rod reciprocal structure transformed from the 6 3 type of Archimedes paving are studied respectively by proposed method and finite element method with ANSYS software. Results shows that the error rate of the nodal forces and nodal displacements between the numerical simulation and the theoretical calculation is less than 5%. The proposed method is not only reliable in static forces calculation, but also simplicity and efficiency in solution process.