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NUMERICAL STUDY OF 3-D ANISOTROPIC PIEZOELECRIC MATERIALS BY BOUNDARY ELEMENT METHOD BASED ON A NEW GREEN FUNCTION
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摘要
Background, Motivation and Objective Because of the electro-mechanical coupling effect, piezoelectric materials have been widely used in high-tech fields such as information, advanced materials and aerospace engineering. Undergoing a high voltage polarization process, commercial piezoelectric ceramics usually behave macroscopic anisotropy. As a traditional numerical method, the boundary element method(BEM) has been successfully applied to deal with the coupling electro-elastic problems in piezoelectric materials. The Green function, as the kernel function of boundary integral equations, is the precondition for the BEM applications. By using the Stroh formalism method, Akamatsu and Tanuma(1997) gave an explicit expression for the 3-D anisotropic piezoelectric Green's function but without its derivatives. The advantage of the Stroh formalism and the residue calculus methods is that they give rise to explicit expressions instead of integral expressions. Following this, Xie et al.(2014) derived an explicit Green's function and its derivatives in terms of the Stroh eigenvalues and eigenvectors for generally anisotropic piezoelectric materials. Based on these expressions, a boundary element method is developed for anisotropic piezoelectric media. It is of great importance for theoretical application to 3-D anisotropic piezoelectric materials. Statement of Contribution/Methods The boundary element method based on a new Green function is used to study the mechanical problems in 3-D anisotropic piezoelectric materials. The new Green function of 3-D anisotropic piezoelectric materials was derived by the Stroh method. Based on this, the displacement boundary integral equation is solved numerically by a collocation method. Then, a classical model for a 3-D piezoelectric cylinder is calculated by the developed boundary element program. Results By using the developed boundary element method, the mechanical and electric variables of 3-D piezoelectric cylinder are obtained and the results are compared with the corresponding analytical solutions and other numerical results by FEM. These results are agreed very well, which shows the effectiveness and high accuracy of the present method. Discussion and Conclusions In this paper, a new type of Green function for 3-D anisotropic piezoelectric materials derived by Xie et al.(2014) is successfully incorporated to a boundary element program. By using this program, the mechanical variables for 3-D cylinders of different piezoelectric materials, PZT-4 and PZT-5H, are calculated under different loading conditions. The numerical results show its precision and efficiency.
Background, Motivation and Objective Because of the electro-mechanical coupling effect, piezoelectric materials have been widely used in high-tech fields such as information, advanced materials and aerospace engineering. Undergoing a high voltage polarization process, commercial piezoelectric ceramics usually behave macroscopic anisotropy. As a traditional numerical method, the boundary element method(BEM) has been successfully applied to deal with the coupling electro-elastic problems in piezoelectric materials. The Green function, as the kernel function of boundary integral equations, is the precondition for the BEM applications. By using the Stroh formalism method, Akamatsu and Tanuma(1997) gave an explicit expression for the 3-D anisotropic piezoelectric Green's function but without its derivatives. The advantage of the Stroh formalism and the residue calculus methods is that they give rise to explicit expressions instead of integral expressions. Following this, Xie et al.(2014) derived an explicit Green's function and its derivatives in terms of the Stroh eigenvalues and eigenvectors for generally anisotropic piezoelectric materials. Based on these expressions, a boundary element method is developed for anisotropic piezoelectric media. It is of great importance for theoretical application to 3-D anisotropic piezoelectric materials. Statement of Contribution/Methods The boundary element method based on a new Green function is used to study the mechanical problems in 3-D anisotropic piezoelectric materials. The new Green function of 3-D anisotropic piezoelectric materials was derived by the Stroh method. Based on this, the displacement boundary integral equation is solved numerically by a collocation method. Then, a classical model for a 3-D piezoelectric cylinder is calculated by the developed boundary element program. Results By using the developed boundary element method, the mechanical and electric variables of 3-D piezoelectric cylinder are obtained and the results are compared with the corresponding analytical solutions and other numerical results by FEM. These results are agreed very well, which shows the effectiveness and high accuracy of the present method. Discussion and Conclusions In this paper, a new type of Green function for 3-D anisotropic piezoelectric materials derived by Xie et al.(2014) is successfully incorporated to a boundary element program. By using this program, the mechanical variables for 3-D cylinders of different piezoelectric materials, PZT-4 and PZT-5H, are calculated under different loading conditions. The numerical results show its precision and efficiency.
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