Trefftz finite element method and its special purpose elements
In this report, the hybrid Trefftz finite element method based on nonsingular T-complete functions is first briefly reviewed for the purpose of establishing notation; then various special purpose elements are developed to illustrat the major advantage of Trefftz methods. In HT-FEM, elements containing local defects are treated by simply replacing the regular T-complete functions with appropriate special purpose trial functions. Elements containing such special trial functions is known as special purpose elements. It should be mentioned that a common characteristic of such special trial functions is that it is not only the governing partial differential equations which are satisfied exactly, but also some prescribed boundary conditions at a particular portion of the element boundary. This enables various singularities to be specifically taken into consideration without troublesome mesh refinement. Formulations of special purpose hole elements for both heat conduction and plane stress/strain problems are presented. Finally, a numerical example involving contact problems with an elliptic hole, are considered. Numerical results from the proposed models are presented and compared with those from ABAQUS.
Finite element method Special purpose element heat conduction Trefftz function
Li Xiao Qing-Hua Qin
Department of Engineering, Australian National University, Canberra, ACT 0200 Australia College of M College of Machinery & Automation, Wuhan University of Science and Technology, Wuhan, 430081 China
国际会议
第三届亚太国际工程中计算方法学术会议暨第五届全国工程中边界元、无网格等数值方法学术会议(ICOME2009)
南京
英文
1-10
2009-10-18（万方平台首次上网日期，不代表论文的发表时间）