An enhanced 8-node isoparametric element with anti-distortion

QIAO Haiqing; BAO Siyuan; SHEN Feng

doi:10.13471/j.cnki.acta.snus.ZR20230003

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An enhanced 8-node isoparametric element with anti-distortion

Research articles | 更新时间：2024-05-30

- An enhanced 8-node isoparametric element with anti-distortion
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 63, Issue 3, Pages: 163-171(2024)
- 作者机构：
  
  苏州科技大学土木工程学院，江苏苏州 215011
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20230003
  CLC： O34
- Published：25 May 2024，
  
  Published Online：24 January 2024，
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乔海青,鲍四元,沈峰.一种抗畸变的增强型八节点等参元[J].中山大学学报(自然科学版)(中英文),2024,63(03):163-171.

QIAO Haiqing,BAO Siyuan,SHEN Feng.An enhanced 8-node isoparametric element with anti-distortion[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(03):163-171.
乔海青,鲍四元,沈峰.一种抗畸变的增强型八节点等参元[J].中山大学学报(自然科学版)(中英文),2024,63(03):163-171. DOI： 10.13471/j.cnki.acta.snus.ZR20230003.

QIAO Haiqing,BAO Siyuan,SHEN Feng.An enhanced 8-node isoparametric element with anti-distortion[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2024,63(03):163-171. DOI： 10.13471/j.cnki.acta.snus.ZR20230003.

摘要

为了提高平面问题的求解精度，基于勒让德正交函数族引入泡状函数来增强映射关系的思想，构造Q8_Legendre单元。针对单元的位移场中含有泡状函数导致单元刚度矩阵规模变大的问题，在得到单元刚度矩阵后附加自由度凝聚，以减小整体刚度矩阵规模、节省计算机内存空间。算例表明，随着泡状函数项数的不断增加，Q8_Legendre单元能够通过分片试验，使得单元的位移精度得到改善，而应力精度保持相当。当出现畸变网格时，Q8_Legendre单元表现出抗畸变的性能，且不会出现闭锁现象。

Abstract

In order to improve the solution precision of the plane problem， the Q8_Legendre element is constructed based on the idea of introducing Bubble function to enhance the mapping relationship based on Legendre orthogonal function. Because the displacement field of the element contains Bubble function， the size of the element stiffness matrix becomes larger. In order to reduce the size of the overall stiffness matrix and save the computer memory space， the additional degrees of freedom are condensed after the stiffness matrix of the element is obtained. Some numerical examples show that the Legendre element can pass the patch test， and the displacement accuracy of the element is improved with the increasing of Bubble function number， while the stress accuracy remains almost the same. When the distortion mesh is encountered， the Q8_Legendre element exhibits the performance of anti-distortion ability， and locking phenomenon does not appear.

关键词

平面问题泡状函数位移修正模型高斯积分抗畸变

Keywords

plane problemBubble functiondisplacement correction modelGauss quadratureanti-distortion

references

岑松，尚闫，周培蕾，等， 2017. 形状自由的高性能有限元方法研究的一些进展［J］. 工程力学， 34（3）：1-14.

龙志飞，岑松， 2001. 有限元法新论：原理·程序·进展［M］. 北京：中国水利水电出版社.

龙驭球，龙志飞，岑松， 2001. 有限元的几个问题和进展［C］//第十届全国结构工程学术会议论文集. 中国力学学会：57-74.

曾攀， 2009. 有限元基础教程［M］. 北京：高等教育出版社.

DING S Y， SHAO G J， HUANG Y Y， et al， 2021. The superconvergence gradient recovery method for linear finite element method with polygons［J］. Int J Numer Methods Eng， 122（16）： 4154-4171.

ESSONGUE S， COUÉGNAT G， MARTIN E， 2021. Finite element modelling of traction-free cracks： Benchmarking the augmented finite element method（AFEM）［J］. Fracture Mechanics， 253：107873.

HAN L， WANG J X ， LI H J， et al， 2020. A time-domain spectral element method with C1 continuity for static and dynamic analysis of frame structures［J］. Structures， 28： 604-613.

HAU N N， KHANH C N， KHUONG D N， et al， 2021. A consecutive-interpolation polyhedral finite element method for solid structures［J］. Int J Numer Methods Eng， 122（20）：5692-5717.

HE D Z， LIU T， 2021. In-plane modal studies of arbitrary laminated triangular plates with elastic boundary constraints by the Chebyshev-Ritz approach［J］. Composite Structures， 271：114138.

HOUMAT A， 1997. Hierarchical finite element analysis of the vibration of membranes［J］. J Sound Vib， 201：465-472.

HOUMAT A， 2000. A triangular Fourier p-element for the analysis of membrane vibrations［J］. J Sound Vib， 230（1）：31-43.

HUANG Y Q， LI Q S， 2004. Four-node incompatible plane and axisymmetric elements with quadratic completeness in the physical space［J］. Int J Numer Methods Eng， 61（10）： 1603-1624.

LEE N S， BATHE K J， 1993. Effects of element distortions on the performance of isoparametric elements［J］. Int J Numer Methods Eng， 36（20）：3553-3576.

LIU G R， DAI K Y， NGUYEN T T， 2007. A smoothed finite element method for mechanics problems［J］. Computational Mechanics， 39（6）：859-877.

LONG Y Q， CEN S， LONG Z F， 2009. Advanced finite element method in structural engineering［M］. Beijing： Tsinghua University Press.

MACNEAL R H， 1989. Toward a defect-free four-noded membrane element ［J］. Finite Elem Anal Des， 5（1）： 31-37.

PIAN T H H， SUMIHARA K， 1984. Rational approach for assumed stress finite elements［J］. Int J Numer Methods Eng， 20（9）：1685-1695.

POZRIKIDIS C， 2014. Introduction to finite and spectral element methods using MATLAB［M］. Chapman and Hall/CRC.

PRZEMIENIECKI J S， 2009. Finite element structural analysis： New concepts［M］. AIAA （American Institute of Aeronautics & Astronautics）.

SOH A K， LONG Y Q， CEN S， 2000. Development of eight-node quadrilateral membrane elements using the area coordinates method［J］. Computational Mechanics， 25（4）：376-384.

SU Z， JIN G Y， YE T G， 2018. Vibration analysis of multiple-stepped functionally graded beams with general boundary conditions［J］. Composite Structures， 186（8）：315-323.

TATYANA S， ZHANG S Y， 2022. An interpolated Galerkin finite element method for the Poisson equation［J］. J Sci Comput， 92（2）：47.

WU C C， CHEUNG Y K， 1995. On optimization approaches of hybrid stress elements［J］. Finite Elem Anal Des， 21（1）：111-128.

ZIENKIEWICZ O C， ZHU J Z， 1992. The superconvergent patch recovery and a posteriori error estimates. Part 1： The recovery technique［J］. Int J Numer Methods Eng， 33（7）：1331-1364.

ZIENKIEWICZ O C， TAYLOR R L， 2005. The finite element method for solid and structural mechanics［M］. Oxford： Elsevier Butterworth-Heinemann.

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