Trefftz Method for Piezoelectricity

In Chapter 3, theoretical solutions for problems of PFC pull-out and push-out are presented. The solutions are, however, restricted to axi-symmetric problems. To remove this restriction, Trefftz numerical methods are presented for solving various engineering problems involved in piezoelectric materials in this chapter. Trefftz methods discussed here include the Trefftz FEM, Trefftz BEM, and the Trefftz boundary-collocation method.

[1]  Qing Hua Qin,et al.  Application of hybrid-Trefftz finite element method to frictional contact problems , 2008 .

[2]  Hui Wang,et al.  Application of hybrid Trefftz finite element method to non‐linear problems of minimal surface , 2007 .

[3]  Qing-Hua Qin,et al.  Variational formulations for TFEM of piezoelectricity , 2003 .

[4]  K. Y. Sze,et al.  Multi-region Trefftz boundary element method for fracture analysis in plane piezoelectricity , 2006 .

[5]  Qing Hua Qin,et al.  Fracture mechanics of piezoelectric materials , 2001 .

[6]  H. Ding,et al.  A boundary integral formulation and 2D fundamental solutions for piezoelectric media , 1998 .

[7]  Qing Hua Qin.  Formulation of hybrid Trefftz finite element method for elastoplasticity , 2005 .

[8]  Yuhong Cui,et al.  Application of Trefftz BEM to anti-plane piezoelectric problem , 2006 .

[9]  Qing Hua Qin,et al.  Hybrid-Trefftz finite element method for Reissner plates on an elastic foundation , 1995 .

[10]  Q. Qin.  Mode III fracture analysis of piezoelectric materials by Trefftz BEM , 2005 .

[11]  Qing Hua Qin,et al.  TRANSIENT PLATE BENDING ANALYSIS BY HYBRID TREFFTZ ELEMENT APPROACH , 1996 .

[12]  Y. Cheung,et al.  Trefftz solutions for piezoelectricity by Lekhnitskii's formalism and boundary‐collocation method , 2006 .

[13]  A. Venkatesh,et al.  Hybrid trefftz plane elasticity elements with p ‐method capabilities , 1992 .

[14]  K. Y. Sze,et al.  Analysis of Electromechanical Stress Singularity in Piezoelectrics by Computed Eigensolutions and Hybrid-trefftz Finite Element Models , 2006 .

[15]  Qing Hua Qin,et al.  The Trefftz Finite and Boundary Element Method , 2000 .

[16]  Q. Qin,et al.  Hybrid Trefftz finite-element approach for plate bending on an elastic foundation , 1994 .

[17]  Qing Hua Qin,et al.  Nonlinear analysis of thick plates by HT FE approach , 1996 .

[18]  Eisuke Kita,et al.  Application of a direct Trefftz method with domain decomposition to 2D potential problems , 1999 .

[19]  Y. Pak,et al.  Crack Extension Force in a Piezoelectric Material , 1990 .

[20]  Q. Qin,et al.  Solving anti-plane problems of piezoelectric materials by the Trefftz finite element approach , 2003 .

[21]  Qing Hua Qin,et al.  MATLAB and C Programming for Trefftz Finite Element Methods , 2008 .

[22]  Biao Wang,et al.  Investigation of anti-plane shear behavior of two collinear cracks in a piezoelectric materials strip by a new method , 2001 .

[23]  S. Diao,et al.  Nonlinear analysis of thick plates on an elastic foundation by HT FE with p-extension capabilities , 1996 .

[24]  Qing Hua Qin,et al.  Application of hybrid-Trefftz element approach to transient heat conduction analysis , 1996 .

[25]  E. Oñate,et al.  The finite element method in the 1990's , 1991 .

[26]  K. Y. Sze,et al.  Trefftz indirect methods for plane piezoelectricity , 2005 .

[27]  E. Stein,et al.  A New Boundary-Type Finite Element for 2D- and 3D-Elastic Solids , 1991 .