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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (6): 660-665.

• 论文 • 上一篇    下一篇

THE ENERGY ORTHOGONAL RELATION BETWEEN CONFORMING AND NON-CONFORMING DISPLACEMENTS OF TRIANGULAR ELEMENT

聂玉峰1, 周天孝2, 聂铁军1   

  1. 1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P. R. China;
    2. Computing Technology Research Institute, CAE, Xi’an 710068, P. R. China
  • 收稿日期:1997-04-28 修回日期:1998-11-07 出版日期:1999-06-18 发布日期:1999-06-18

THE ENERGY ORTHOGONAL RELATION BETWEEN CONFORMING AND NON-CONFORMING DISPLACEMENTS OF TRIANGULAR ELEMENT

Nie Yufeng1, Zhou Tianxiao2, Nie Tiejun1   

  1. 1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, P. R. China;
    2. Computing Technology Research Institute, CAE, Xi’an 710068, P. R. China
  • Received:1997-04-28 Revised:1998-11-07 Online:1999-06-18 Published:1999-06-18

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摘要： Based on the variational principle of combinative stability,combined hybrid methods posed by Zhou Tianxiao are absolutely convergent and stabilized. Zhou has advocated a systematic approach to enhanced stress/strain schemes and has designed a family of lower-order elements which are affine-equivalent to n-cube (n=2,3).The energy orthogonal relation between the conforming part and the non-conforming part of displacements interpolation functions in triangular element is given,in which the stress is interpolated by linear polynomials on each element,but the displacements are interpolated by the sum of conforming linear and nonconforming quadratic polynomials.Furthermore,this element is equivalent to the conforming triangular linear element,that is,the non-conforming parts have no contribution to enhanced strains.

关键词: combinative stability, energy orthogonality, enhanced strain

Abstract: Based on the variational principle of combinative stability,combined hybrid methods posed by Zhou Tianxiao are absolutely convergent and stabilized. Zhou has advocated a systematic approach to enhanced stress/strain schemes and has designed a family of lower-order elements which are affine-equivalent to n-cube (n=2,3).The energy orthogonal relation between the conforming part and the non-conforming part of displacements interpolation functions in triangular element is given,in which the stress is interpolated by linear polynomials on each element,but the displacements are interpolated by the sum of conforming linear and nonconforming quadratic polynomials.Furthermore,this element is equivalent to the conforming triangular linear element,that is,the non-conforming parts have no contribution to enhanced strains.

Key words: combinative stability, energy orthogonality, enhanced strain

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