Engineering Transactions, 64, 4, pp. 485–491, 2016
10.24423/engtrans.758.2016

### Solution of the Three Forces Problem in a Case of Two Forces Being Mutually Orthogonal

Tomasz SOKÓŁ
Warsaw University of Technology
Poland

Tomasz LEWIŃSKI
Warsaw University of Technology
Poland

The present paper delivers some new numerical and exact solutions of the three forces problem which is one of fundamental problems of Michell’s truss theory. The problem is to find the lightest fully stressed truss transmitting three self-equilibrated co-planar forces. In this study we limit our considerations to the case of two forces being mutually orthogonal. The aim of the paper is to classify possible layouts of optimal trusses depending on the position of the applied lateral point load (the positions of the other two forces are fixed, which, however, does not restrict the scope of the study). The exact analytical solutions are obtained with a great help of numerical solutions which enable proper prediction of the optimal layouts
Keywords: topology optimization; Michell trusses; three forces problem
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DOI: 10.24423/engtrans.758.2016