20-Node Rational Elements for 3D Anisotropic Elastic Problems

MAO Ling; YAO Wei-an; GAO Qiang; ZHONG Wan-xie

doi:10.3879/j.issn.1000-0887.2014.06.001

Volume 35 Issue 6

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Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(6): 589-597

MAO Ling, YAO Wei-an, GAO Qiang, ZHONG Wan-xie. 20-Node Rational Elements for 3D Anisotropic Elastic Problems[J]. Applied Mathematics and Mechanics, 2014, 35(6): 589-597. doi: 10.3879/j.issn.1000-0887.2014.06.001

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20-Node Rational Elements for 3D Anisotropic Elastic Problems

doi: 10.3879/j.issn.1000-0887.2014.06.001

State Key Laboratory of Structural Analysis for Industrial Equipment;Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024,P.R.China

Funds: The National Basic Research Program of China (973 Program)（2010CB832704）；The National Natural Science Foundation of China（11372065）

Received Date: 2014-01-16
Rev Recd Date: 2014-03-21
Publish Date: 2014-06-11

Abstract

Abstract

For the conventional finite element method, only the geometry and node locations of elements were considered in the interpolation functions, while the physical parameters which reflect the key features of the physical problems were ignored, so its numerical performance may be not satisfying in some cases. The construction of the rational finite element method was different from that of the conventional finite element method. The linear combinations of the fundamental solutions to the problem’s controlling differential equations were used as the interpolation functions, so the stress and strain fields were interpolated directly in the physical domain at the same time. The transfer matrix was modified at the element level to pass the patch test, and the resulting element stiffness matrix was related closely to the physical parameters of the problem. The rational finite element avoids the separation between the mathematical and physical aspects of a problem, so the stability and accuracy of numerical analysis could be improved significantly. Two kinds of 20-node rational brick elements based on the principle of minimum potential energy and satisfying the requirements of the patch test, were constructed according to the fundamental solutions to general 3D anisotropic problems. Numerical examples show that the rational elements give numerical results with not only high accuracy, but also good numerical stability.
- general anisotropy,
- rational finite element,
- 20-node brick element

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References(14)

References

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