Structural optimization of guyed trusses

Abstract

HERE is a strong trend in the design of skeletal structures to, wherever practical, make increasing use of tensioned cables. One of the best examples of the convergence of structural efficiency to a best design can probably be found when studying the evolution of the configurations of power transmission towers. From the early days of cantilever truss structures these have now evolved to the much lighter rope type in which two separate vertical cable-stayed lattice struts support the power conductors through suspension from a cross rope. Apart from the savings in material, significant savings in transportation cost can also be obtained especially since erection often has to occur in remote areas. Although the cable-stayed structures are easy to analyze, the determination of a best or least weight design can be complex due to the variety of design variables available. These are, typically, configuration, geometry, member sizing, and prestraining. The optimization of a configuration is complex and is best accomplished manually, perhaps with the aid of layout optimization methods. On the contrary, geometric and prestrain optimization and sizing can be treated by direct sensitivity analysis of a chosen topology. This paper describes the sizing and prestrain optimization of guyed trusses. For the nonlinear analysis the total Lagrangian method is used in combination with the pure Newton method and adaptive arc-length procedures. Because of the lack of stiffness of a cable structure in its undeformed state, soft spring elements are used to stabilize the structure temporarily during the load stepping phase. The choice of prestrain instead of prestress variables is justified by both the simplicity of inclusion of prestrain in the sensitivity analysis and by the independence of the prestrain quantity with respect to the sequence of pretensioning of the structure. The prestraining of a member can also simply be seen as the lack of fit of a member in a fixed geometry and can, in practice, be accomplished by specifying member lengths to create a predetermined lack of fit or by specifying turns of a turnbuckle included in the member. For the optimization process, two optimization methods are used, namely, the sequential quadratic programming (SQP) method IDESIGN (PLBA) authored by Arora1 and the successive approximation method (SAM) algorithm of Snyman and Stander2 and Stander et al.3 Using two methods gives optima in which greater confidence can be placed. Additionally, some idea of the degree of difficulty of the newly formulated optimization problems is gained. Five examples are given to demonstrate the analysis and optimization methodology. The optimization of example structures subjected to second-order effects show that unexpected results can be obtained. A number of papers,48 related to the general topic of the sensitivity analysis and optimization of structures with nonlinear geometric