Equivalent-force density method as a shape-finding tool for cable-membrane structures

Cable-membrane structure is a kind of flexible tension structures, of which both cables and membranes are lack of bending and compressing stiffness. In order to reduce the nonlinearity and the strong coupling between its geometric shape and internal stress distribution to improve the computational efficiency and convergence, this paper developed an equivalent-force density method by identifying the equivalent axial force density and equivalent transversal force density to replace the prestress in triangular and quadrilateral membrane elements. Then the method was applied as a shape-finding tool for cable-membrane structure. Furthermore, several numerical simulations, including planar cable-membrane structure, catenoid and umbrella/tent-like cable-membrane structures, were conducted to confirm the efficiency and robustness of the proposed method.