Abstract
Materials and microstructures with specific configurations are able to have negative Poisson’s ratio. This paper proposes a topology optimization methodology of frame structures to design a planar periodic structure that exhibits negative Poisson’s ratio. Provided that beam section of each existing member is chosen from a set of some given candidates, we can reduce the topology optimization problem to a mixed-integer linear programming problem. Since the proposed approach treats frame structures and stress constraints are rigorously addressed, the optimal solution contains no hinge region. A heuristic method with local search is used to solve large-scale problems. Numerical examples and fabrication test demonstrate that planar periodic frame structures exhibiting negative Poisson’s ratio can be successfully obtained by the proposed method.
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