The Modified Dynamic Relaxation Method for the Form-Finding of Membrane Structures

摘要

In this manuscript, the dynamic relaxation method for the form-finding of membrane structures has been modified in two aspects. First, a simple procedure to find the damping coefficient value directly has been proposed. The results, which are determined using examples, show that the damping coefficient value obtained using the procedure is close to the critical damping coefficient. Second, the applicable range of the method has been extended to meet the architects' expectation of more shapes. Through analysis of an HP-type membrane, the function f (L) = (d/L)~α has been introduced to calculate the nodal initial stress stiffness, in which α is the control parameter that is dependent on the initial equilibrium shape and α > 0; d is the average mesh (triangular element) length; and L is the length of the edge of the triangular element. Then the shape of the membrane can be controlled effectively. The corresponding membrane shapes can be obtained with different values of the parameter α. In this manner, the application of the classic dynamic relaxation method can be extended.