Optimization of Redundant Prestressed Structures

The load index approach to structural optimization is extended to similar or mixed element systems with statically determinate or redundant prestressed configurations and under multiple load conditions. Employing component optimization expressions reduces the problem to an unconstrained search through a space defined in terms of variables which express the relative orientation of component elements and the redundant loads. It is shown that a minimum weight truss may be prestressed redundant under a single external load condition if the internal prestress is considered as a separate load condition, i.e., the truss must not fail under the internal prestress in the absence of the applied load. Multiple load truss applications show that additional weight savings over previous analyses can be realized by optimizing bar orientation and redundant load. Optimizing of redundant loads, however, will in general require a turnbuckle in series with a flexible spring in order to maintain a unique prestress under multiple load conditions.