This technology proposed a new numerical analysis method for a minimizing problem of functional of two phase system based on the phase-field method using level set model that can allow shape and topological change.  In addition, the new structural optimization method based on the new numerical analysis method is proposed, and the method is expanded to minimizing the mean compliance problem.  First, the basic concept of conventional level set method and phase-field method are explained, and extended phase-field method is constructed using level set model.  Next, a new structural optimization method based on the extended phase-field method is explained, and minimum mean compliance problem is formulated.  Next, a oputimization algorithm for a structural optimization based on the extended phase-field method is constructed.  Finally, several examples are provided to confirm the usefulness of the proposed structural optimization method.   

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