Trefftz methods for plane piezoelectricity

• Autorzy: Sze K. Y. , Jin W. G. , Sheng N. , Li J.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

Starting from the governing equations, the general solution and the complete solution set for plane piezoelectricity are derived in this paper. Subsequently, the Trefftz collocation method (TCM) is formulated. TCM falls into the category of Trefftz indirect methods which adopt the truncated complete solution set as the trial functions. Similar to the boundary element method, the solution procedure of TCM requires only boundary discretization. Numerical examples are presented to illustrate the efficacy of the formulation.

Słowa kluczowe

EN

Trefftz method; piezoelectricity

PL

Trefftz method; piezoelektryczność

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 619--627
• Opis fizyczny: Bibliogr. 23 poz., tab., rys.

Twórcy

autor

Sze K. Y.

• Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, P. R. China

autor

Jin W. G.

• Department of Mechanics & Engineering Science, Fudan University, Shanghai, P. R. China

autor

Sheng N.

• Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong, P. R. China

autor

Li J.

• Department of Mechanics & Engineering Science, Fudan University, Shanghai, P. R. China

Bibliografia

• [1] Z.K. Wang, B.L. Zheng. The general solution of three-dimensional problems in piezoelectric media. International Journal of Solids and Structures, 32: 105-115, 1995.
• [2] H.J. Ding, B. Chen, J. Liang. General solutions for coupled equations for piezoelectric media. International Journal of Solids and Structures, 33: 2283-2298, 1996.
• [3] M.L. Dunn, H.A. Wienecke. Green's functions for transversely isotropic piezoelectric solids. International Journal of Solids and Structures., 33: 4571-4581, 1996.
• [4] E. Pan, F. Tonon. Three-dimensional Green's functions in anisotropic piezoelectric solids. International Journal of Solids and Structures, 37: 943-958, 2000.
• [5] J.S. Lee and L.Z. Jiang. A boundary integral formulation and 2D fundamental solution for piezoelastic media. Mechanics Research Communications, 21: 47-54, 1994.
• [6] H.J. Ding, G.Q. Wang, W.Q. Chen. A boundary integral formulation and 2D fundamental solutions for piezoelectric media. Computer Methods in Applied Mechanics and Engineering, 158: 65-80, 1998.
• [7] P. Lu, O. Mahrenholtz. A variational boundary element formulation for piezoelectricity. Mechanics Research Communications, 21: 605-611, 1994.
• [8] T. Chen, F.Z. Lin. Boundary integral formulations for three-dimensional anisotropic piezoelectric solids. Computational Mechanics, 15: 485-496, 1995.
• [9] E. Pan. A BEM analysis of fracture mechanics in 2D anisotropic piezoelectric solids. Engineering Analysis with Boundary Elements, 23: 67-76, 1999.
• [10] M. Denda, J. Lua. Development of the boundary element method for 2D piezoelectricity. Composites Part B: Engineering, 30: 699-707, 1999.
• [11] I. Herrera. Trefftz method. In: C.A. Brebbia, editor, Topics in Boundary Element Research. Springer, New York, 1984
• [12] A.P. Zielinski, O.C. Zienkiewicz. Generalized finite element analysis with T-complete boundary solution functions. International Journal for Numerical Methods in Engineering, 21: 509-528, 1985.
• [13] Y.K. Che ung, W.G. Jin, O.C. Zienkiewicz. Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions. Communications in Applied Numerical Methods, 5: 159-169, 1989.
• [14] Y.K. Cheung, W.G. Jin, O.C. Zienkiewicz. Solution of Helmholtz equation by Trefftz method. International Journal for Numerical Methods in Engineering, 32: 63-78, 1991.
• [15] W.G. Jin, Y.K. Cheung, O.C. Zienkiewicz. Application of the Trefftz method in plane elasticity problems. International Joumal for Numerical Methods in Engineering, 30: 1147-1161, 1990.
• [16] W.G. Jin, Y.K. Cheung, O.C. Zienkiewicz. Trefftz method for Kirchhoff plate bending problems. International Journal for Numerical Methods in Engineering, 36: 765-781, 1993.
• [17] E. Kita, N. Kamiya, Y. Ikeda. Boundary-type sensitivity analysis scheme based on indirect Trefftz formulation. Advances in Engineering Software, 24: 89-96, 1995.
• [18] J. Jirousek, A. Wroblewski. T-elements: a finite element approach with advantages of boundary solution methods. Advances in Engineering Software, 24(71-88), 1995.
• [19] H.Q. Zhang. A united theory on general solutions of systems of elasticity equations (in Chinese). Journal of Dalian University of Technology, 3: 23- 47, 1978.
• [20] R.A. Eubanks, E. Sternberg. On the axisymmetric problem of elastic theory for a medium with transverse isotropy. Journal of Rational Mechanics and Analysis, 3: 89-101, 1954.
• [21] I. Herrera. Boundary Method: An Algebraic Theory. Pitman, Boston , 1984.
• [22[ S.B. Park, C.T. Sun. Effect of electric field on fracture of piezoelectric ceramics. International Journal of Fracture, 70: 203-216, 1995.
• [23] H. Sosa. Plane problems in piezoelectric media with defects. International Journal of Solids and Structures, 28: 491-505, 1991.