Analysis of cable - membrane structures using the Dynamic Relaxation Method

This paper compares the effectiveness of different schemes of dynamic relaxation method (DRM) for the analysis of cable and membrane structures. DRM is an iterative process that is used to find static equilibrium. DRM is not used for the dynamic analysis of structures; a dynamic solution is used for a fictitious damped structure to achieve a static solution. The stability of the method depends on the fictitious variables (i.e. mass a damping) and time step. The effect of mass distribution along the structure is also studied in the paper. Eight different schemes DRM will be used in this paper. Schemes A and B are based on the theory of viscous damping. Schemes C, D and E are based on the theory of kinetic damping (KD) with a peak in the middle of the time step and schemes F, G and H are based on the theory of KD with parabolic approximation. A cable is approximated as a tension bar, a catenary (several tension bars) and a perfectly flexible element. For membrane structures a triangular element is considered. The chosen methods are applied to six constructions. The cable structures are analyzed in Examples 1 to 3, the membrane structures are analyzed in Examples 4 to 6. The results imply that that it is impossible to determine the best scheme. In this context, it may be noticed that the methods based on kinetic damping appear more stable and faster. For bar element, catenary and cable elements the results confirm that it is beneficial to divide the same amount of mass into all nodes of the structure proportionally to the stiffest node of the solved structure (schemes C and F). For membrane element it is preferred to use the kinetic damping method with the approximation of the kinetic energy peak in the middle of the time step Delta t.