Trefftz Finite Element Analysis of Axisymmetric Potential Problems in Orthotropic Media
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摘要: Trefftz有限元法(Trefftz finite element method, TFEM)因其独特的优良品质而备受关注.针对正交各向异性轴对称位势问题,提出了一种4节点四边形环状单元.在该单元模型中,首先假设两套独立的位势插值模式:即单元域内场和网线场,然后代入修正变分泛函并利用Gauss散度定理消除区域积分,最后根据驻值原理导得只含边界积分的单元刚度方程.数值算例表明了该单元的准确性、稳定性以及对网格畸变的不敏感性.
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关键词:
- Trefftz有限元法 /
- 修正变分泛函 /
- 位势问题 /
- 轴对称 /
- 正交各向异性介质
Abstract: Trefftz finite element method (TFEM) has received considerable attention due to its excellent feasures. A four-node quadrilateral annular element was proposed for analyzing axisymmetric potential problems in orthotropic media. In the element model, two independent potential interpolation modes, namely intraelement field and frame field, were firstly assumed. Then, they were both substituted into the modified variational functional and the domain integral involved was eliminated using the Gaussian divergence theorem. Finally, the element stiffness equation including boundary integrals only was derived based on the stationary principle. Numerical examples demonstrate that the developed element is accurate, stable and insensitive to mesh distortion. -
[1] Jirousek J, Leon N. A powerful finite element for plate bending[J].Computer Methods in Applied Mechanics and Engineering,1977,12(1): 77-96. [2] Trefftz E. Ein Gegenstück zum Ritz’schen Verfahren[C]//Proceedings of the 2nd International Congress on Applied Mechanics.Zurich, Switzerland, 1926: 131-137. [3] Qin Q H.The Trefftz Finite and Boundary Element Method [M]. Southampton: WIT Press, 2000. [4] Qin Q H, Wang H.MATLAB and C Programming for Trefftz Finite Element Methods [M]. Boca Raton: CRC Press, 2008. [5] Jirousek J, Venkatesh A. Hybrid Trefftz plane elasticity elements withp method capabilities[J].International Journal for Numerical Methods in Engineering,1992,35(7): 14431472. [6] Wang H, Qin Q H, Arounsavat D. Application of hybrid Trefftz finite element method to nonlinear problems of minimal surface[J].International Journal for Numerical Methods in Engineering,2007,69(6): 1262-1277. [7] Fu Z J, Qin Q H, Chen W. HybridTrefftz finite element method for heat conduction in nonlinear functionally graded materials[J].Engineering Computations: International Journal for ComputerAided Engineering and Software,2011,28(5): 578-599. [8] Cao L L, Wang H, Qin Q H. Fundamental solution based graded element model for steadystate heat transfer in FGM[J].Acta Mechanica Solida Sinica,2012,25(4): 377-392. [9] Wang K Y, Zhang L Q, Li P C. A fournode hybridTrefftz annular element for analysis of axisymmetric potential problems[J].Finite Elements in Analysis and Design,2012,60: 49-56. [10] 赵新娟, 赵吉义. 位势问题的杂交有限元算法研究[J]. 中原工学院学报, 2011,22(1): 59-61. (ZHAO Xin-juan, ZHAO Ji-yi. Potential problems in anisotropic solids using hybrid finite element model[J].Journal of Zhongyuan University of Technology,2011,22(1): 59-61. (in Chinese)) [11] 王克用, 李培超, 张敏良. 正交各向异性位势问题的Trefftz有限元法[J]. 力学季刊, 2012,33(3): 499-506. (WANG Ke-yong, LI Pei-chao, ZHANG Min-liang. Trefftz finite element method for orthotropic potential problems[J].Chinese Quarterly of Mechanics,2012,33(3): 499506. (in Chinese)) [12] Marczak R J, Denda M. New derivations of the fundamental solution for heat conduction problems in threedimensional general anisotropic media[J].International Journal of Heat and Mass Transfer,2011,54(15/16): 3605-3612.
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