Two-scale asymptotic errors analysis for piezoelectric problem in periodic structure of composites

The fields of applications and design for piezoelectric effect grew rapidly in recent years, and these materials play an important role in countless areas of modern life. There are few analysis and results for piezoelectric problems in periodic structures in composites. By means of two-scale method, the two-scale asymptotic expansions for the displacement and the potential for structure of composites with small periodic configuration under piezoelectric condition are constructed, and the coupled relation between the displacement field and the electric field within periodic cell is built, and the approximate errors of displacement and potential are presented. As a result, one new asymptotic method of computing approximate solutions of the displacement and the potential in periodic piezoelectric structure is proposed.