期刊文献+

基于辛弹性力学解析本征函数的有限元应力磨平方法 被引量:6

A stress recovery method based on the analytical eigenfunctions of symplectic elasticity
下载PDF
导出
摘要 在实际工程结构的结构强度与优化等力学数值分析中,应力计算结果的精度是非常重要的。有限元法是得到最广泛应用的一类数值方法,并形成了众多通用的有限元程序系统。这些程序系统采用的几乎都是基于最小总势能的位移法,虽然其分析给出的有限元位移场具有较高的精度,但所得到的有限元应力场的精度较位移场大大降低。基于极坐标辛对偶体系所提供的平面弹性力学的解析辛本征展开解,并借用有限元程序系统所得到的节点位移,本文提出了一个应力分析的改进方法。数值结果表明,本方法给出的应力分析精度得到大幅提高,并具有良好的数值稳定性,可用于有限元程序系统的后处理,以提高应力尤其是关键区域应力的分析精度。 The accuracy of stress is important in the engineering application analysis, such as structural strength,structural optimization,etc. The Finite Element Method (FEM) is one of the most widely ap- plied numerical methods based on which many general program systems have been built. The displace- ment method based on the minimum total potential energy principle is commonly used for these FEM program systems. So the displacement field of high accuracy can be obtained. However,it would lead to a stress field of much lower accuracy comparing with the displacement field obtained. In this paper,a stress recovery method is presented to improve the result of stress analysis,which make use of the symplectic eigenfunctions of plane problems in the polar coordinate system and node displacements provided by FEM. Numerical results show that, the new technique improve evidently accuracy of stress analysis and the numerical stability is also very well. Hence,it could be applied for the postprocessing of the general program system of FEM to improve the accuracy of stress analysis, especially the accuracy of stress on the key area.
出处 《计算力学学报》 EI CAS CSCD 北大核心 2012年第4期511-516,共6页 Chinese Journal of Computational Mechanics
基金 国家自然科学基金(10772039) 973国家重点基础研究计划(2010CB832704)资助项目
关键词 有限元 应力磨平 辛弹性力学 解析解 FEM stress recovery symplectic elasticity analytical solution
  • 相关文献

参考文献9

  • 1Zienkewicz R Taylor. The Finite Element Method [M] . 42^th ed. MeGraw2Hill,N Y, 1989.
  • 2J T Oden, H J Brauchli. On the calculation of consistent stress distributions in finite element approximations[J]. Int. J. Numer. Methods Engrg. , 1971,3 (3) : 317-325.
  • 3E Hinton,J S Campbell. Local and global smoothing of discontinuous finite element functions using a least squares methods[J], lnt. J. Numer. Methods Engrg. , 1974,8(3) :461-480.
  • 4J T Oden,J N Reddy. Note on an approximate method for computing consistent conjugate stresses in elastic finite elements[J]. Int. J. Numer. Methods Engrg. , 1973,6(1):55-61.
  • 5J Barlow. Comment on 'Optimal stress locations in finite element models' [J]. Int. J. Numer. Methods Engrg. ,1977,11(3) :604.
  • 6O C Zienkiewicz,Zhu J Z. The superconvergent patch recovery and a posteriori error estimates(Part 1) :The recovery technique[J]. Int. J. Nurner. Methods Engrg. , 1992,33(7) :1331-1364.
  • 7Zhang Z, A Naga. A new finite element gradient recovery method:Superconvergenee property[J]. SIAM J. Sci. Comput. ,2005,22(4) :1192-1213.
  • 8孙雁,钟万勰.有限元表面应力计算[J].计算力学学报,2010,27(2):177-181. 被引量:7
  • 9Yao W A,Zhong W X,Lim C W. Symplectic Elasticity[M]. Singapore :World Scientific, 2009.

二级参考文献6

  • 1Zienkewicz R. Taylor, The Finite Element Method [M]. 4-th ed. McGraw-Hill, NY, 1989.
  • 2Timoshenco S P, Goodier J N. Theory of Elasticity [M]. McGraw-Hill, 1970.
  • 3姚伟岸,钟万勰.辛弹性力学.[M].北京:高等教育出版社,2003.
  • 4Pian T H H.(卞学鐄).Derivation of element stiffness matrices by assumed stress functions[-J]. AIAA J, 1964,7(2) : 1333-1336.
  • 5Chang H H. On the approximate solutions of boundary value problems at a point[J]. Science Record, 1952, 5:1-4 .
  • 6孙雁,钟万勰.有限元表面应力计算[J].计算力学学报,2010,27(2):177-181. 被引量:7

共引文献6

同被引文献49

  • 1江守燕,杜成斌,顾冲时,陈小翠.求解双材料界面裂纹应力强度因子的扩展有限元法[J].工程力学,2015,32(3):22-27. 被引量:15
  • 2王承强,郑长良.平面裂纹应力强度因子的半解析有限元法[J].工程力学,2005,22(1):33-37. 被引量:13
  • 3钟万勰,徐新生,张洪武.弹性曲梁问题的直接法[J].工程力学,1996,13(4):1-8. 被引量:8
  • 4袁驷,林永静.二阶非自伴两点边值问题Galerkin有限元后处理超收敛解答计算的EEP法[J].计算力学学报,2007,24(2):142-147. 被引量:27
  • 5Brinson L C, Lammering R. Finite element analysis of the behavior of shape memory alloys and their applications[ J]. International Journal of Solids and Structures, 1993, 30 ( 23 ) : 3261-3280.
  • 6Burton D S, Gao X, Brinson L C. Finite element simulation of a serf-healing shape memory alloy composite[J]. Mechanics of Materials, 2007, 38(5/5): 525-537.
  • 7Tanaka K. A thermomechanical sketch of shape memory effect: one-dimensional tensile be- havior [ J ]. Res Mechanica, 1985, 18 : 251-253.
  • 8Liang C, Rogers C A. One-dimensional thermomechanical constitutive relations for shape memory materials[J]. Journal of lnteUigent Material Systems and Structures, 1990, 1(2) : 207-234.
  • 9Boyd J G, Lagoudas D C. A thermodynamic constitutive model for the shape memory materi- als-part I : the monolithic shape memory alloys [ J ]. International Journal of Plasticity, 1996, 12(5): 805-842.
  • 10Lagoudas D C, Bo Z, Qidwai M A. A unified thermodynamic constitutive model for SMA and finite element analysis of active metal matrix composites[J]. Mechanics of Advanced Materi- als and Structures, 1996, 3(2) : 153-179.

引证文献6

二级引证文献5

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部