Material with negative Poisson's ratio is called auxetic material. We call a structure exhibiting similar behavior is a auxetic structure. This paper discusses topology optimization for finding auxetic frame structures. Particularly, we consider a frame unit of a planar periodic microstructure. Based upon the conventional ground structure method, the optimization problem is formulated as a mixed integer linear programming (MILP) problem that maximizes the output displacement when the displacement of the input node is prescribed. The MILP problem is solved globally by using, e.g., a branch-and-cut method. Numerical experiments demonstrate that the proposed method can find planar frames such that ratio of output displacement to input displacement is less than -0.5.
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