Progress in Civil and Structural Engineering Computing
Chapter 6 A.S.K. Kwan
Cardiff School of Engineering, Cardiff University, United Kingdom Keywords: cable structures, geometric nonlinearity, prestressed mechanisms. 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. This paper therefore seeks not only to present a new and fast analytical technique, but also has as one of its aims to illustrate simplicity in the fundamental behaviour of geometrically nonlinear cable structures. It shall be seen therefore that the proposed technique itself requires only relatively straightforward understanding of structural mechanics. Indeed, the initial presentation of the technique is to decouple the governing mechanics from the numerical solution so that even an undergraduate engineer with access to standard numerical packages or libraries (e.g. MATLAB or NAG) would be able to understand the principles involved in Sections 3 and 4, and proceed to analyse simple three-dimensional structures such as those in this paper, with thirty or forty lines of coding. The value of the proposed technique however, is not only in its simplicity. Since the governing equations are directly the equilibrium and compatibility conditions of the cable net, it shall be shown that given the correct iterative approach, they are capable of converging rapidly on the correct solution. This iterative approach requires the decomposition of a load into two components, one which `excites' the structural mechanism and the other which does not. Accuracy and speed comparisons are made with illustrative examples. | ||||||||||
