Structural Dynamic Analysis Using the Cell-Based Smoothed Point Interpolation Method(CS-PIM)with Virtual Points

doi:10.7652/xjtuxb201811021

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Structural Dynamic Analysis Using the Cell-Based Smoothed Point Interpolation Method(CS-PIM)with Virtual Points

更新时间：2025-07-09

- Structural Dynamic Analysis Using the Cell-Based Smoothed Point Interpolation Method(CS-PIM)with Virtual Points
- Vol. 52, Issue 11, Pages: 142-149(2018)
- 作者机构：
  
  1. 大连理工大学船舶工程学院,辽宁,大连,116024
  2. 大连理工大学工业装备与结构分析国家重点实验室,辽宁,大连,116024
  3. 高新船舶与深海开发装备协同创新中心,上海,200240
- 作者简介：
- 基金信息：
- DOI：10.7652/xjtuxb201811021
  CLC： O241.82
- Online First：10 November 2018，
  
  Published：2018
- 稿件说明：
移动端阅览
Structural Dynamic Analysis Using the Cell-Based Smoothed Point Interpolation Method(CS-PIM)with Virtual Points[J]. 2018, 52(11): 142-149.
DOI：

Structural Dynamic Analysis Using the Cell-Based Smoothed Point Interpolation Method(CS-PIM)with Virtual Points[J]. 2018, 52(11): 142-149. DOI： 10.7652/xjtuxb201811021.

摘要

为了解决有限元方法采用线性三角形单元时系统刚度过硬、导致结构动力学分析中求得的结构固有频率过高的问题

采用结合虚拟点的单元基光滑点插值方法(CS-PIM)进行结构动力学分析

通过对虚拟点数量与位置的调整

提高了浓缩形函数的精度

在不增加计算成本的情况下

克服了传统虚拟点布置方法中存在的系统刚度过软、固有频率值过低以及存在虚假模态等时间不稳定现象

能够准确模拟系统刚度

为动力学分析提供精确且稳定的解。该方法使用可以自动划分的线性三角形背景网格离散问题域

对复杂形状的问题适应性强

操作简便

具有良好的工程应用前景。

Abstract

To overcome overly-stiff property existing in the widely used finite element method(FEM)with linear triangular elements

which generally leads much higher natural frequency

the cell-based smoothed point interpolation method(CS-PIM)with condensed shape functions is applied to structural dynamic analysis. Adopting the condensed shape function constructed with the new scheme of virtual nodes arrangement

which increases the accuracy of shape functions

the present method can avoid the temporal instability problems

including the much lower natural frequency and spurious natural mode caused by the overly-soft property in CS-PIM using traditional virtual nodes arrangement. In the present method the simple linear triangular mesh can automatically discretize the domain. This method can provide stable and highly accurate solutions to dynamic analysis of complex engineering structures.

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references

ZIENKIEWICZ O C, TAYLOR R L, FOX D A. The finite element method: vol 1 [M]. 5th ed. Oxford, UK: Butterworth/Heinemann, 2000: 58-60.

ZHANG Z Q, LIU G R. Upper and lower bounds for natural frequencies: a property of the smoothed finite element methods [J]. International Journal for Numerical Methods in Engineering, 2010, 84(2): 149-178.

ZHANG Z Q, LIU G R. Solution bound and nearly exact solution to nonlinear solid mechanics problems based on the smoothed FEM concept [J]. Engineering Analysis with Boundary Elements, 2014, 42(2): 99-114.

LIU G R, ZHANG G Y. Smoothed point interpolation methods: G space theory and weakened weak forms [M]. Singapore: World Scientific, 2013: 305-306.

LIU G R. A G space theory and a weakened weak(W2)form for a unified formulation of compatible and incompatible methods: part I Theory [J]. International Journal for Numerical Methods in Engineering, 2010, 81(9): 1093-1126.

LIU G R. A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods [J]. International Journal of Computational Methods, 2008, 5(2): 199-236.

彭金晓. 光滑点插值无网格法及在工程力学中的应用 [D]. 长春: 吉林大学, 2011: 19-21.

徐旭, 周敏敏, 于东元, 等. 一种应变重构点插值无网格方法(SC-PIM)[J]. 吉林大学学报(理学版), 2011, 49(6): 969-972.

XU Xu, ZHOU Minmin, YU Dongyuan, et al. A strain constructed point interpolation method(SC-PIM)[J]. Journal of Jilin University(Science Edition), 2011, 49(6): 969-972.

鲁欢, 于大鹏, 张桂勇, 等. 应用点基局部光滑点插值法的固有频率上下界计算 [J]. 西安交通大学学报, 2017, 51(5): 165-172.

LU Huan, YU Dapeng, ZHANG Guiyong, et al. Node-locally-based smoothed point interpolation method for calculating upper lower bounds of natural frequency [J]. Journal of Xi'an Jiaotong University, 2017, 51(5): 165-172.

杜超凡, 章定国. 光滑节点插值法: 计算固有频率下界值的新方法 [J]. 力学学报, 2015, 47(5): 839-847.

DU Chaofan, ZHANG Dingguo. Node-based smoothed point interpolation method: a new method for computing lower bound of natural frequency [J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(5): 839-847.

LIU Y J, ZHANG G Y, LU H, et al. A cell-based smoothed point interpolation method(CS-PIM)for 2D thermoelastic problems [J]. International Journal of Numerical Methods for Heat and Fluid Flow, 2017, 27(6): 1249-1265.

CHENG J, CHANG X L, WU S C, et al. Certified solutions for hydraulic structures using the node-based smoothed point interpolation method(NS-PIM)[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2010, 34(15): 1560-1585.

WU S C, LIU G R, CUI X Y, et al. An edge-based smoothed point interpolation method(ES-PIM)for heat transfer analysis of rapid manufacturing system [J]. International Journal of Heat and Mass Transfer, 2010, 53(9): 1938-1950.

ZHANG G Y, LIU G R. Meshfree cell-based smoothed point interpolation method using isoparametric PIM shape functions and condensed RPIM shape functions [J]. International Journal of Computational Methods, 2011, 8(4): 705-730.

WANG J G, LIU G R. A point interpolation meshless method based on radial basis functions [J]. International Journal for Numerical Methods in Engineering, 2002, 54(11): 1623-1648.

刘桂荣, 顾元通. 无网格法理论及程序设计 [M]. 济南: 山东大学出版社, 2007: 23-24.

SMITH I M, GRIFFITHS D V, MARGETTS L. Programming the finite element method [M]. 5th ed. New York, USA: Wiley, 2015: 109-110.

妥吉英,邓兆祥,张河山,等.新型扭转准零刚度的振动角度传感系统.2017,51(8):90-95.[doi:10.7652/xjtuxb201708 015]

鲁欢,于大鹏,张桂勇,等.应用点基局部光滑点插值法的固有频率上下界计算.2017,51(5):165-172.[doi:10.7652/xjtuxb201705023]

张鸿志,周强,陈刚,等.气动弹性系统本征正交分解降阶模型精度的参数影响研究.2016,50(11):104-109.[doi:10.7652/xjtuxb201611016]

张西宁,吴吉利,王奔.一种利用起车过程瞬态振动响应的转子动力学参数识别方法.2016,50(7):1-6.[doi:10.7652/xjtuxb201607001]

满兴博,伍晓红,孙清.采用非线性Galerkin方法的柔性梁模型降阶研究.2015,49(7):113-119.[doi:10.7652/xjtuxb 201507019]

马驰骋,张希农,罗亚军,等.变质量矩形贮箱流固耦合系统动力学特性分析.2014,48(7):109-116.[doi:10.7652/xjtuxb201407019]

张静,郭宏伟,刘荣强,等.空间含铰可展桁架结构的非线性动力学建模与分析.2013,47(11):113-119.[doi:10.7652/xjtuxb201311020]

方兵,张雷,赵继,等.轴承结合部动态参数识别与等效分析模型的研究.2012,46(11):69-74.[doi:10.7652/xjtuxb2012 11014]

孟庆虎,孟庆丰,朱永生,等.用于机械系统固有频率及阻尼比计算的改进频域方法.2015,49(8):1-5.[doi:10.7652/xjtuxb201508001]

陶庆,孙文磊,周建星.考虑齿圈柔性的行星传动系统固有特性与灵敏度研究.2015,49(3):113-120.[doi:10.7652/xjtuxb201503018]

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