Optimum number of actuators to minimize the cross-sectional area of prestressable cable and truss structures

This paper describes a new computational method for determining the optimum number of actuators to design the optimal and economic cross-sectional area of pin-jointed assemblies based on the conventional force method. The most active members are selected to be prestressed to redistribute stress in the whole structure, resulting in regulating the internal force of bars that face high stress. Reducing stress in critical members allows the designers to select smaller cross-sectional areas than before. Furthermore, the maximum absolute displacement of the structures before the optimization is set as a limit for the displacement of the optimized structures. The derived equations from the force method are subjected to the optimization algorithms (i.e., sequential quadratic pro-gramming (SQP), trust-region reflective, active set, and interior point) to minimize the necessary number of actuators for prestressing. The optimization procedure is done in two ways: first, by minimizing the number of actuators for prestressing through implementing the fmincon function, and second, by selecting the most economical area via prestressing the structure before loading. The method is applied to the numerical models of two cable and four truss structures that were previously studied. The outcomes show that by actuating as few actuators as possible, the area of cable and truss structures can be minimized up to 17% and 27 %, respectively. Moreover, 5% improvement can be obtained applying the current technique to the optimized trusses by quoted methods. The outcomes are compared with results from the literature. Moreover, the results obtained from MATLAB are verified by SAP2000 software.