Initial equilibrium solution methods for cable reinforced membranes part I-formulations

This paper describes the initial equilibrium problem for tension structures and presents a variety of methods for solving it. Two least squares techniques are presented in which the prestress distribution in the reference configuration is the problem unknown and the reference shape is explicitly defined by the designer. The existing force density method is shown to be a special case of the new assumed geometric stiffness method where both the reference shape and prestress distribution are unknowns in the solution. The iterative smoothing technique allows the designer to solve for the shape of the reference configuration in terms of an assumed prestress distribution. Also, an extension of the nonlinear displacement analysis method is presented which is based on a special slip formulation which accounts for relative movement between membranes and other structural components. Finally, the possibility of a combined solution process is discussed.