Effect of Compatibility and Prestressing on Optimized Trusses

Abstract

Assuming force method analysis formulation, the effect of compatibility conditions on optimal design of trusses is studied. Neglecting the latter conditions, a linear programming (LP) formulation is obtained. The possibility of applying prestressing forces by “lack of fit” to maintain compatibility at the LP optimum is demonstrated. It has been shown that for structures subjected to a single loading condition, the LP lower‐bound solution is the final optimum. Prestressing might be required to maintain compatibility in cases where the optimal solution represents a statically indeterminate structure. The various possible solutions for structures subjected to multiple loading conditions are discussed. It is shown that under certain circumstances, compatibility conditions can be satisfied at the LP optimum only by applying different sets of prestressing forces for the various loadings. For certain geometries, the LP solution represents multiple optimal topologies, part of them being statically determinate structures. In such cases, the LP lower‐bound solution is the final optimum, and no prestressing is required to maintain compatibility. In cases where compatibility conditions considerably affect the solution, prestressing by lack of fit might significantly improve the final optimum.