Development of 2D Hybrid Equilibrium Elements in Large Increment Method

doi:10.1007/s12204-013-1384-3

Abstract

Abstract: As a force-based finite element method (FEM), large increment method (LIM) has been developed in recent years. It has been shown that LIM provided prominent advantage of parallel computation with high efficiency and low time consumption for member structural system. To fully utilize its advantage in parallel computation, it is the time to extend LIM to 2D and 3D continua analysis. In this paper, a 2D finite element library with the capability of modeling arbitrary configurations is developed. Some illustrative numerical examples are solved by using the proposed library; the obtained results are compared with those obtained from both traditional displacement-based FEM and analytical solutions, which has clearly shown the advantages of LIM.

Key words: large increment method (LIM)| hybrid equilibrium element| finite element method (FEM)| 2D elements

摘要： As a force-based finite element method (FEM), large increment method (LIM) has been developed in recent years. It has been shown that LIM provided prominent advantage of parallel computation with high efficiency and low time consumption for member structural system. To fully utilize its advantage in parallel computation, it is the time to extend LIM to 2D and 3D continua analysis. In this paper, a 2D finite element library with the capability of modeling arbitrary configurations is developed. Some illustrative numerical examples are solved by using the proposed library; the obtained results are compared with those obtained from both traditional displacement-based FEM and analytical solutions, which has clearly shown the advantages of LIM.

关键词: large increment method (LIM)| hybrid equilibrium element| finite element method (FEM)| 2D elements

CLC Number:

LONG Dan-binga* (龙丹冰), LIU Xi-lab (刘西拉). Development of 2D Hybrid Equilibrium Elements in Large Increment Method[J]. Journal of shanghai Jiaotong University (Science), 2013, 18(2): 205-215.

References

[1] Zhang Chun-jun. A large increment method for material nonlinearity problems [D]. Beijing: Department of Civil Endineering, Tsinghua University, 1996 (in Chinese).
[2] Zhang Chun-jun, Liu Xi-la. A large increment method for material nonlinearity problems [J]. Advances in Structural Engineering, 1997, 1(2): 99-109.
[3] Liu Xi-la, Wang Kai-jian, Zhang Chun-jun. The large increment method for nonlinear elastic problems of truss systems [J]. Engineering Mechanics, 2005, 22(sup 1): 7-15 (in Chinese).
[4] Barham W S, Aref A J, Dargush G F. On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach [J]. International Journal of Solids and Structures, 2008, 45: 5688-5704.
[5] Wang Kai-jian. Network parallel computation based on the large increment method [D]. Beijing: Department of Civil Engineering, Tsinghua University, 2004 (in Chinese).
[6] Liu Xi-la, Long Dan-bing. A novel parallelized structural analysis method: Large increment method [C]// Proceeding of 1st Engineering Design and the Application of HPC Technique. Shanghai, China: China Civil Engineers Society, 2007: 16-29 (in Chinese).
[7] Guo Zao-yang, Long Dan-bin, Liu Xi-la, et al. A force-based large increment method for continuum elastoplastic problems [C] // Proceedings of 17th Association of Computational Mechanics in Engineering Nottingham. UK: Association of Computational Mechanics in Engineering, 2009.
[8] Long Dan-bin, Guo Zao-yang, Liu Xi-la, et al. An element nodal force-based large increment method for elastoplasticity [C] // Proceedings of ISCM II and EPMESC XII. Hong Kong-Macau, China: American Institute of Physics, 2009: 1401-1405.
[9] Kaljevic I, Patnaik S N, Hopkins D A. Development of finite elements for two-dimensional structural analysis using the integrated force method [J] . Computers & Structures, 1996, 59(4): 691-706.

[1]	ZHANG Peizhen, LIN Fang. Sound Scattering Characteristics of Oxygen Cylinder for Open Breathing Diver [J]. Journal of Shanghai Jiao Tong University, 2022, 56(6): 764-771.
[2]	MA Zunnong, ZHANG Yansong, ZHAO Yixi. Mechanism and Influencing Factors of Frictional Energy Dissipation in Multilayer Ultrasonic Welding [J]. Journal of Shanghai Jiao Tong University, 2022, 56(6): 772-783.
[3]	ZHU Hanhao, XIAO Rui, ZHU Jun, TANG Jun. Propagation Characteristics of Low Frequency Sound Energy in Range-Dependent Shallow Water Waveguides [J]. Journal of Shanghai Jiao Tong University, 2021, 55(8): 958-967.
[4]	ZHANG Yuan, LI Fanchun, JIA Dejun. Design and 3D Printing Simulation of a Lattice Compressor Impeller [J]. Journal of Shanghai Jiao Tong University, 2021, 55(6): 729-740.
[5]	JING Mengjie (荆梦杰), CUI Zhixin(崔志鑫), FU Hang (傅航), CHEN Xiaojun (陈晓军). Real-Time Deformation Simulation of Kidney Surgery Based on Virtual Reality [J]. J Shanghai Jiaotong Univ Sci, 2021, 26(3): 290-297.
[6]	YE Liyu, WANG Chao, GUO Chunyu, CHANG Xin. Strength Check Method of Blade Edge Under Concentrated Ice Load Condition [J]. Journal of Shanghai Jiaotong University, 2020, 54(1): 10-19.
[7]	YING Hongwei,SHEN Huawei,ZHANG Jinhong,ZHU Chengwei. Semi-Analytical Solution of Limit Support Pressure on Shield Tunnel Face Subjected to Water Level Fluctuation [J]. Journal of Shanghai Jiaotong University, 2018, 52(8): 982-990.
[8]	SUN Shuangshuang，WU Dan，LIU Dongdi. Dynamic Finite Element Analysis on a Composite Hollow Beam Embedded with Pseudoelastic Shape Memory Alloy Fibers [J]. Journal of Shanghai Jiaotong University, 2018, 52(7): 845-852.
[9]	DUAN Li1,GAO Junchao1,WANG Ruijun2,HU Mingkai1,SU Jingchao3 CHENG Qingqing3,ZHANG Bo3,YUAN Tao2. Simulation Analysis of Temperature Distribution of Turbine Blades by Thermal Buffer Coating for Aero Engine [J]. Journal of Shanghai Jiaotong University, 2017, 51(8): 915-920.
[10]	ZHANG Yang1,2,CHEN Bing1,ZHAO Shexu1,LI Siping1. Numerical Simulation of Axially Loaded Circular Steel Tubular Stub Columns with Fly Ash Concrete Infill [J]. Journal of Shanghai Jiaotong University, 2017, 51(7): 769-773.
[11]	LU Ping1a,1b,ZHANG Yunkai1a,1b,CHEN Bo2. Finite Element Method Simulation of Stagger Power Spinning Forming of Automobile Spoke [J]. Journal of Shanghai Jiaotong University, 2015, 49(01): 56-61.
[12]	JIA Hong-xue1* (贾红学), LONG Dan-bing2 (龙丹冰), LIU Xi-la3 (刘西拉). Development of the Large Increment Method in Analysis for Thin and Moderately Thick Plates [J]. Journal of shanghai Jiaotong University (Science), 2014, 19(3): 265-273.
[13]	ZHANG Zi-xin1* (张子新), SHEN Mang-jie1 (沈铓杰), TENG Li2 (滕丽). Back-Analysis of the Response of Shield Tunneling by 3D Finite Element Method [J]. Journal of shanghai Jiaotong University (Science), 2013, 18(3): 298-305.
[14]	WANG Yiming,ZHANG Mengxi,QIU Chengchun,LI Lin. Numerical Analysis of Embankment Reinforced with H-V Reinforcement under Traffic Loading [J]. Journal of Shanghai Jiaotong University, 2013, 47(09): 1459-1463.
[15]	LAI Huahui1a,ZHU Jiwen2,WANG Yingyi1b,HUANG Xingchun1a,1b. Analysis of Displacement of Soft Soil and Its Application Considering the Rheological Property [J]. Journal of Shanghai Jiaotong University, 2013, 47(09): 1419-1423.