1. Liaoning Provincial Engineering Lab for Deep-Sea Floating Structures, School of Naval Architecture Engineering, Dalian University of Technology, Dalian 116024, China;
2. State Key Lab of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China;
3. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China;
4. School of Navigation and Marine Engineering, Dalian Ocean University, Dalian 116023, China
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.
[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.
