Analysis of geometrically nonlinear cable structures

A new direct, fast, and non-linear approach to the static analysis of geometrically nonlinear cable structures is presented. The approach involves the derivation of the equilibrium and compatibility relationships of a simple bar element which undergoes large displacements. An algorithm is presented whereby an externally applied load is decomposed into two separate components corresponding to the extensional and inextensional displacements of the structure, where the former is treated using ordinary matrix methods and the latter is solved using the approach introduced in this paper. While the method is iterative, the solution is rapid because the iterative procedure has been specially devised with large displacement statical analysis in mind. Several illustrative examples are provided, including accuracy comparison with results in the literature as well as timing comparisons with the Dynamic Relaxation method, a technique generally held with high esteem by practitioners. The technique introduced would be of use to all geometrically nonlinear structural problems (e.g. shell and fabric structures), but has been devised specifically for the commonly found prestressed cable structures.