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A minimization problem of a square error in relation to a given deformation and an active deformation is formulated for a linear elastic structure. To solve this problem the homogenized elastic constants are employed and a topology optimization is replaced with an optimal density distribution problem, using the similar method proposed by Bends\u03b8e and Kikuchi. The homogenized elastic constants are calculated by the homogenization method for a microstructure having a rectangular hole. 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