Some Aspects of the Application of Dynamic Relaxation Method in Space Structures

Abstract

Dynamic relaxation method (DRM) is a powerful method to solve problems such as form-finding and buckling analysis of flexible structures. In this paper, some aspects of the application of DRM in the analysis of flexible structures are discussed. In the first part, the application of DRM in form finding analysis of systems with one degree of freedom and systems with multiple degrees of freedom are described. The reason why only the geometrical stiffness of system is considered is explained. For cable-nets and tensile membrane structures the final shape is determined by the orientation of their internal force vector and the magnitude of the internal force vector only affects the base period of the system. So the convergence speed of DRM in form finding problem can be improved by augmenting the magnitude of internal force vector. Two examples, one is a two bar system and the other is a cable net, are analyzed and the numerical results prove this point well. The application of DRM in the buckling analysis is also discussed in the second part. Considering the main difference between FEM and DRM, a new local arc-length method based on DRM is proposed. Compared with the traditional arc-length method, the new one has good convergence and needs less computer memory for computing. The good convergence is also verified by two conventional numerical examples in the buckling analysis of spatial structures. The work here will benefit the further research of DRM.