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

Authors:
Tomasz Sokół;George I. Rozvany
Affiliations:
Department of Structural Mechanics and Computer Aided Engineering, Faculty of Civil Engineering, Warsaw University of Technology, Warsaw, Poland 00-637;Department of Structural Mechanics, Budapest University of Technology and Economics, Budapest, Hungary 1521
Venue:
Structural and Multidisciplinary Optimization
Year:
2012

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Abstract

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.