Analysis of new wave-curved tensegrity dome

•A new wave-curved tensegrity dome with special topology is explored.•A novel LM-QN form-finding method for cable-strut structure is proposed.•Feasible prestress is optimized by secondary form-finding and section design.•Static analyses indicate characteristic of linearity under increasing loads.•Dynamic performances show the satisfactory stability of the structure. The cable dome is one of the most widely used structures in cable-strut tensile structures. A new topology of the tensegrity system is firstly proposed, and combined with the circular wave surface, a new wave-curved tensegrity dome is then obtained, which has less members than traditional cable domes. Concurrently, based on a combination of Levenberg-Marquardt and quasi-Newton (LM-QN) methods, a form-finding algorithm for cable-strut tensile structures is proposed to solve nonlinear equilibrium equations by addressing the least-squares problem. Subsequently, the configuration of the wave-curved tensegrity dome is analyzed using the proposed form-finding method, which demonstrates that an integral feasible prestress exists in the new structural form. Finally, the static and dynamic performance of the new structure are analyzed, and its possible defects and weaknesses are subsequently examined based on the analysis results. The numerical results show that the proposed wave-curved tensegrity dome satisfies the necessary requirements and has high research relevance as a type of light roof. Moreover, the LM-QN method can overcome the singular problem of the tangent stiffness matrix and be used as one of the form-finding methods for the verification of new structures.