Abstract
This paper deals with optimization of planar frames under a topological constraint to realize the frames in the form of a one-dimensional complex called Tree. The tree has no loops and its number of connected components is one. In other words, its zero-dimensional homology group is isomorphic to an additive group of integers. and its one-dimensional homology group is equal to zero. The constraint consisting of the homology groups is satisfied by use of a generalized inverse matrix and the optimum structure is found by genetic algorithm. It will be possible to apply the method of treatment for the tree proposed in this paper to various meaningful topological constraints. Minimization of the total strain energy of tree frames is employed as a numerical example to verify the validity of the proposed method.
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