New analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports

Extending some results by Sokol and Lewinski (Struct Multidisc Optim 42:835---853, 2010), the optimal topology of bi-symmetric trusses with two symmetrically placed pointloads is determined analytically, and verified by highly accurate numerical calculations. It is rather remarkable that Michell's best-known classical solution had to wait over hundred years for its generalization from one to two point loads. Some implications of these solutions, including properties of so-called O-regions, are also discussed.