A Meshless Natural Element Method for 2D Viscoelastic Problems

CHEN Shen-shen; ZHONG Bin

doi:10.21656/1000-0887.370300

Volume 38 Issue 5

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CHEN Shen-shen, ZHONG Bin. A Meshless Natural Element Method for 2D Viscoelastic Problems[J]. Applied Mathematics and Mechanics, 2017, 38(5): 605-612. doi: 10.21656/1000-0887.370300

Citation:

CHEN Shen-shen, ZHONG Bin. A Meshless Natural Element Method for 2D Viscoelastic Problems[J]. Applied Mathematics and Mechanics, 2017, 38(5): 605-612. doi: 10.21656/1000-0887.370300

Citation:

CHEN Shen-shen, ZHONG Bin. A Meshless Natural Element Method for 2D Viscoelastic Problems[J]. Applied Mathematics and Mechanics, 2017, 38(5): 605-612. doi: 10.21656/1000-0887.370300

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A Meshless Natural Element Method for 2D Viscoelastic Problems

doi: 10.21656/1000-0887.370300

School of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, P.R.China

Funds: The National Natural Science Foundation of China(11462006；21466012)

Received Date: 2016-09-29
Rev Recd Date: 2016-11-22
Publish Date: 2017-05-15

Abstract

Abstract

Based on the meshless natural element method, a new algorithm was proposed to solve 2D viscoelastic problems. According to the elasticviscoelastic correspondence principle and the Laplace transform technique, the viscoelastic problem was transformed into an elastic problem in the Laplace space and then the basic formula of the natural element method for the analysis of viscoelastic problems were derived. As a recently developed meshless method, the natural element method (NEM) is essentially a Galerkin method based on natural neighbour interpolation. Compared to most other meshless methods, the shape function employed in the NEM has interpolation property and its support domain is anisotropic. Some numerical examples verify the effectiveness of the developed method.
- meshless method,
- natural element method,
- viscoelasticity,
- correspondence principle,
- Laplace transform

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References(18)

References

[1]	Naguib H E, Park C B. A study on the onset surface melt fracture of polypropylene materials with foaming additives[J]. Journal of Applied Polymer Science,2008,109(6): 3571-3577.
[2]	陈兵兵, 徐赵东, 朱一强, 等. 加入粘弹性阻尼器的高楼桅杆风振响应分析[J]. 华东交通大学学报, 2014,31(5): 77-85.(CHEN Bing-bing, XU Zhao-dong, ZHU Yi-qiang, et al. Wind vibration response analysis of high building masts with viscoelastic dampers[J]. Journal of East China Jiaotong University,2014,31(5): 77-85.(in Chinese))
[3]	Sladek J, Sladek V, Zhang Ch, et al. Meshless local Petrov-Galerkin method for continuously nonhomogeneous linear viscoelastic solids[J]. Computational Mechanics,2006,37: 279-289.
[4]	祝彦知, 薛保亮, 王广国. 粘弹性地基上粘弹性地基板的自由振动解析[J]. 岩石力学与工程学报2002,21(1): 112-118.(ZHU Yan-zhi, XUE Bao-liang, WANG Guang-guo. Free vibration analysis of viscoelastic foundation plate on viscoelastic foundation[J]. Chinese Journal of Rock Mechanics and Engineering,2002,21(1): 112-118.(in Chinese))
[5]	Christensen R M. Theory of Viscoelasticity [M]. New York: Academia Press, 1971.
[6]	姚伟岸, 杨海天, 高强. 平面粘弹性问题的辛求解方法[J]. 计算力学学报, 2010,27(1): 14-20.(YAO Wei-an, YANG Hai-tian, GAO Qiang. A new approach to solve plane viscoelastic problems in the symplectic space[J]. Chinese Journal of Computational Mechanics,2010,27(1): 14-20.(in Chinese))
[7]	丁睿, 姚林泉, 李挺. 粘弹性薄板动力响应问题的多重互易法[J]. 工程数学学报, 2005,22(6): 1006-1012.(DING Rui, YAO Lin-quan, LI Ting. Multiple reciprocity method for solving dynamics response of viscoelastic thin plate[J]. Chinese Journal of Engineering Mathematics,2005,22(6): 1006-1012.(in Chinese))
[8]	Belytschko T, Lu Y Y, Gu L. Element-free Galerkin method[J]. International Journal for Numerical Methods in Engineering,1994,37(2): 229-256.
[9]	王伟, 伊士超, 姚林泉. 分析复合材料层合板弯曲和振动的一种有效无网格方法[J]. 应用数学和力学, 2015,36(12): 1274-1284.(WANG Wei, YI Shi-chao, YAO Lin-quan. An effective meshfree method for bending and vibration analyses of laminated composite plates[J]. Applied Mathematics and Mechanics,2015,36(12): 1274-1284.(in Chinese))
[10]	孙新志, 李小林. 复变量移动最小二乘近似在Sobolev空间中的误差估计[J]. 应用数学和力学, 2016,37(4): 416-425.(SUN Xin-zhi, LI Xiao-lin. Error estimates for the complex variable moving least square approximation in Sobolev spaces[J]. Applied Mathematics and Mechanics,2016,37(4): 416-425.(in Chinese))
[11]	秦义校, 程玉民. 温度场分析的重构核粒子边界无单元法[J]. 机械工程学报, 2008,44(6): 95-100.(QIN Yi-xiao, CHENG Yu-min. Reproducing kernel particle boundary element-free method for temperature field problems[J]. Chinese Journal of Mechanical Engineering,2008,44(6): 95-100.(in Chinese))
[12]	Braun J, Sambridge M. A numerical method for solving partial differential equations on highly irregular evolving grids[J]. Nature,1995,376: 655-660.
[13]	Sukumar N, Moran T, Belytschko T. The natural element method in solid mechanics[J].International Journal for Numerical Methods in Engineering,1998,43(5): 839-887.
[14]	张勇, 易红亮, 谈和平. 求解辐射导热耦合换热的自然单元法[J]. 工程热物理学报, 2013,34(5): 918-922.(ZHANG Yong, YI Hong-liang, TAN He-ping. Natural element method for coupled radiative and conductive heat transfer[J]. Journal of Engineering Thermophysics,2013,34(5): 918-922.(in Chinese))
[15]	江涛, 章青. 直接增强自然单元法计算应力强度因子[J]. 计算力学学报, 2010,27(2): 264-269.(JIANG Tao, ZHANG Qing. Computing stress intensity factor by enriched natural element method[J]. Chinese Journal of Computational Mechanics,2010,27(2): 264-269.(in Chinese))
[16]	曾祥勇, 朱爱军, 邓安福. Winkler地基上厚板分析的自然单元法[J]. 固体力学学报, 2008,29(2): 163-169.(ZENG Xiang-yong, ZHU Ai-jun, DENG An-fu. Natural element method for analysis of thick plates lying over Winkler foundations[J]. Chinese Journal of Solid Mechanics,2008,29(2): 163-169.(in Chinese))
[17]	Stehfest H. Algorithm 368: numerical inversion of Laplace transform[J]. Communications of the ACM,1970,13(1): 47-49.
[18]	Sim W J, Kwak B M. Linear viscoelastic analysis in time domain by boundary element method[J]. Computers & Structures,1988,29(4): 531-539.