Geometrical aspects of optimum truss like structures for three-force problem
In this paper, similarities between three-force and three-point non-smooth optimization problems are highlighted. Starting from geometrical rules controlling discrete optimum solutions for three-point problems a reasonable hypothesis is created for similar geometrical rules to control discrete optimum structures for three-force problems. The hypothesis is confirmed through a numerical approach. A step-by-step method to graphically obtain a discrete optimum structure for any set of three balanced forces is provided. It is shown that discrete optimum structures with large number of elements converge to the known continuum optimum solutions in the literature.
KeywordsDiscrete optimum Three-point problem Three-force problem Optimum truss Michell truss Hencky Net
I would like to thank William F. Baker of Skidmore, Owings and Merrill, LLP and Dr. Cenk Tort of Mitaş Engineering for continuing support and advice. Without these two individuals writing this paper would not be possible. Also, I would like to thank Prof. G. H. Paulino, Ms. L. Stromberg and the rest of the TOP Gang at University of Illinois in Champaign, who are the experts in the field of topology optimization, for their valuable suggestions and opinions.
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