Abstract
This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM. Numerical examples are presented to highlight the accuracy of the proposed CS-XFEM with the analytical solutions and the XFEM results.
Highlights
Because of their inherent coupling of electric and mechanical behaviors, piezoelectric materials have been widely used in sensors, actuators, signal transmitters and surface acoustic wave devices, aerospace panels, and civil structures
It is obvious that the cell-based smoothed extended finite element method (CS-XFEM) can produce more accurate results than XFEM when using the same number of nodes, which indicates that the smoothing technique adopted in this work improve the calculation of normalized mechanical and electrical intensity factors for fracture in piezoelectric materials
The results prove that the CS-XFEM can decrease stiffness of the system and improve solution accuracy
Summary
This paper presents a cell-based smoothed extended finite element method (CS-XFEM) to analyze fractures in piezoelectric materials. The method, which combines the cell-based smoothed finite element method (CS-FEM) and the extended finite element method (XFEM), shows advantages of both methods. The crack tip enrichment functions are specially derived to represent the characteristics of the displacement field and electric field around the crack tip in piezoelectric materials. With the help of the smoothing technique, integrating the singular derivatives of the crack tip enrichment functions is avoided by transforming interior integration into boundary integration. This is a significant advantage over XFEM.
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