基于点基局部光滑点插值法的结构动力分析

PDF(2616 KB)

振动与冲击 ›› 2018, Vol. 37 ›› Issue (17) : 241-248.

论文

基于点基局部光滑点插值法的结构动力分析

张桂勇1,2,3，鲁欢1，王海英4，于大鹏1，孙铁志1

作者信息 +

Structural dynamic analysis using NPSPIM

ZHANG Guiyong1,2,3,LU Huan1,WANG Haiying4,YU Dapeng1,SUN Tiezhi1

Author information +

文章历史 +

摘要

针对传统有限元法采用线性三角形单元刚度过硬、计算的固有频率值较大，四边形单元对复杂构件不能自动剖分，点基光滑点插值法刚度过软、会导致计算动力问题失败以及求解固有频率值过低的问题，提出了点基局部光滑点插值法(NPS-PIM)。该方法将有限元与点基光滑点插值法结合，对背景网格基础上形成的点基光滑域剖分、进行局部应变光滑，计算结构的动力问题。研究发现，该方法克服了点基光滑点插值法的时间不稳定性和求解固有频率值过低的缺陷；在采用同样线性三角形单元网格对问题域进行离散的情况下，方法计算得到的固有频率较传统有限元法有明显提高。该方法简便实用、易于实现，具有较好的工程应用前景。

Abstract

Aiming at problems of linear triangular element used by the traditional finite element method (FEM) having an over-hard stiffness and computed structure natural frequencies being larger,while the node-based smooth point interpolation method (NS-PIM) causing over-soft stiffness and making dynamic computation failure and computed natural frequencies too smaller,a node-based partly smoothed point interpolation method (NPS-PIM) was proposed here. This new method combined FEM and NS-PIM through partly strain smoothing operation to compute structural dynamic problems. It was shown that the proposed method overcomes NS-PIM’s deficiencies of time instability and solved natural frequencies too smaller; the same linear triangular element mesh was used to discretize a problem domain,the natural frequencies computed with the new method are more accurate than those with the traditional FEM; the new method is simple and easy to implement,and it has better prospects for engineering application.

导出引用

张桂勇1,2,3，鲁欢1，王海英4，于大鹏1，孙铁志1. 基于点基局部光滑点插值法的结构动力分析[J]. 振动与冲击, 2018, 37(17): 241-248

ZHANG Guiyong1,2,3,LU Huan1,WANG Haiying4,YU Dapeng1,SUN Tiezhi1. Structural dynamic analysis using NPSPIM[J]. Journal of Vibration and Shock, 2018, 37(17): 241-248

参考文献

[1] Pian T H H, wu C C. Hybrid and Incompatible Finite Element Methods[M]. (CRC Press, Boca Raton), 2006.
[2] 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, 2008a, 5(2): 199-236.
[3] Liu G R. A weakened weak (W2) form for a unified formulation of compatible and incompatible methods, Part I; Theory and Part II: Applications to solid mechanics problems[J]. International Journal for Numerical Methods in Engineering (revised), 2008b.
[4] 张桂勇，宗智，Gu Y T，等. 无网格光滑点插值法[J]. 中国力学学会计算力学专业委员会.中国计算力学大会2014暨第三届钱令希计算力学奖颁奖大会论文集[C].中国力学学会计算力学专业委员会:,2014:1.
   Zhang Guiyong, ZongZhi, Gu Y T, et al. Smooth point interpolation meshless method [J]. Mechanical professional committee of the institute of computational mechanics in China. China 2014 and the third conference on computational mechanics makes money and computational mechanics awards conference proceedings [C]. China mechanical professional committee of the institute of computational mechanics:, 2014:1
[5] Liu G R, Zhang G Y. Upper bound solution to elasticity problems: A unique property of the linearly conforming point interpolation method (LC-PIM)[J]. International Journal for Numerical Methods in Engineering, 2008a, 74: 1128-1161.
[6] Zhang G Y, Liu G R, Nguyen T T, et al. The upper bound property for solid mechanics of the linearly conforming radial point interpolation method (LC-RPIM)[J]. International Journal of Computational Methods, 2007a, 4(3): 521-541.
[7] 彭金晓. 光滑点插值无网格法及在工程力学中的应用[D]吉林：吉林大学，2011.
     Peng Jinxiao. Smooth point interpolation meshless method and its application in engineering mechanics [D]. Jilin: Jilin university, 2011.
[8] 陈善群，廖斌，李海峰. 有限差分/无网格方法耦合生成混合算法研究(英文)[J]. 船舶力学,2011,09:969-980.
    Chen Shan-qun, Bin Liao, li hai-feng. Finite difference coupling meshless method study the hybrid algorithm (English) [J]. Journal of ship mechanics, 2011,09:969-980.
[9] Liu G R, Nguyen-Thoi T, Lam K Y. An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids[J]. J Sound Vib, 2009, 320: 1100-1130.
[10] Zhang Z Q, Liu G R. Temporal stabilization of the node-based smoothed finite element method (NS-FEM) and solution bound of linear elastostatics and vibration problems[J]. Computational Mechanics, 2010, 46(2): 229-246.
[11] Liu GR, Zhang GY, Smoothed Point Interpolation Methods: G space and weakened weak forms”, World Scientific (Singapore), 2013.
[12] DOKUMACI E. On super accurate finite elements and their duals for eigenvalue computation [J]. Journal of Sound and Vibration, 2006, 298(1-2): 432-438.
[13] Zienkiewicz O C, taylor R L. The Finite Element Method 5th edn[M].(Butterworth Heinemann, Oxford, UK), 2000.
[14] G. R. LIU, G. Y. ZHANG. A NORMED G SPACE AND WEAKENED WEAK (W2) FORMULATION OF A CELL-BASED SMOOTHED POINT INTERPOLATION METHOD[J]. International Journal of Computational Methods, 2009, 6(01):147-179.
[15] Gu Y T, Liu G R. A meshless local Petrov-Galerkin (MPLG) method for free and vibration analyses for solids[J]. Computational Mechanics, 2001, 27 (2001): 188-198.
[16] Brebbia C A, Telles J C, Wrobel L C. Boundary Element Techniques[M]. Springer, Berlin, 1984.