Hierarchically decomposed finite element method for the coupled four fields of the fluid-structure–piezoelectric–circuit interaction

Abstract

A partitioned iterative method based on hierarchical decomposition is proposed for providing numerical modeling and analysis of the piezoelectric energy harvester which is involved in coupled fluid-structure interaction, coupled electro-mechanical, and a controlling electrical circuit for piezoelectric structural applications in energy harvesting. This circuitintegrated piezoelectric structural application in energy harvesting surrounded by fluid media takes the form of natural four-way coupling of fluid flow, the structure, the electromechanical effect of the piezoelectric material, and the electrical circuit. This can be formulated exactly as a fluid-structure-piezoelectric-circuit interaction. These coupled four fields are hierarchically decomposed into the fluid-structure interaction, structure-piezoelectric interaction, and piezoelectric-circuit interaction interactions. Then these subsystems are decomposed into each field. The proposed finite element method enables to reuse of existing techniques because of its modularity. Furthermore, scalability to multiphysics and multisystem couplings is expected. There are some numerical approaches in particular monolithic coupling methods are studied which are computationally expensive and leads to an ill-conditioned coefficient matrix. Nevertheless, accurate modeling for predicting the characteristics of this four-way coupling using partitioned methods has not yet been developed. This method enables an investigation of piezoelectric structures in fluid with complex geometry, material composition, and attached electrical circuits to the harvester. A flexible piezoelectric bimorph harvester in the converging channel is analyzed to demonstrate the efficiency of the proposed method. The results indicate that the method captures the coupled effect accurately.

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