Efficiency of dynamic relaxation methods in form-finding of tensile membrane structures

The main idea of this study is to investigate and compare the efficiency of the dynamic relaxation methods (DRMs) in the form-finding of tensile membrane structures (TMSs). The form-finding process as a main stage in the design and construction of TMSs has been considered for finding an equilibrium configuration subjected to a specific prestress distribution. DRMs as a pseudo-dynamic analysis are an explicit iterative technique for the nonlinear analysis of structures. In the techniques, the static equilibrium of structures is solved by integrating the pseudo-dynamic equations in order to obtain the steady state of the pseudo-dynamic problem. In this study, the efficiency and generality performance of DRMs are compared through solving three selected TMSs. In order to achieve this purpose, seven schemes of the DR approach are selected based on combining the fictitious parameters including the time step, diagonal mass, and damping matrices which were proposed in the previous studies. Furthermore, a reference index is proposed by combining the total number of iterations and the overall duration of analysis in order to appropriately compare the schemes of the DR approach in the form-finding of TMSs.