Trusses are load-carrying light-weight structures consisting of bars connected at joints ubiquitously applied in a variety of engineering scenarios. Designing optimal trusses that satisfy functional specifications with a minimal amount of material has interested both theoreticians and practitioners for more than a century. In this paper, we introduce two main ideas to improve upon the state of the art. First, we formulate an alternating linear programming problem for geometry optimization. Second, we introduce two sets of complementary topological operations, including a novel subdivision scheme for global topology refinement inspired by Michells famed theoretical study. Based on these two ideas, we build an efficient computational framework for the design of lightweight trusses. AD{We illustrate our framework with a variety of functional specifications and extensions. We show that our method achieves trusses with smaller volumes and is over two orders of magnitude faster compared with recent state-of-the-art approaches.
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