Research Paper

Structural and Multidisciplinary Optimization

, Volume 46, Issue 4, pp 477-486

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • Tomasz SokółAffiliated withDepartment of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology Email author 
  • , George I. N. RozvanyAffiliated withDepartment of Structural Mechanics, Budapest University of Technology and Economics


Extending some results by Sokół and Lewiński (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.


Exact topology optimization Michell trusses Optimal regions Symmetry Stress constraints