轴对称构件受力分析的插值粒子法

杜红秀; 魏宏; 秦义校; 李中华; 王同尊

doi:10.7498/aps.64.100204

摘要

面对土木工程与机械工程中广泛存在的轴对称力学问题, 采用具有离散点插值特性的无网格方法形函数, 结合弹性力学空间轴对称问题的最小势能原理, 建立了轴对称构件力学分析的插值粒子法. 本文无网格法方法构造形函数不依赖网格, 也具有像有限元法一样可直接施加边界条件的优点. 本方法能直接获得全域连续应力场, 避免了有限元法应力后处理二次拟合带来的计算误差. 最后通过实例分析, 验证了所建立的无网格方法的有效性.

关键词:

Abstract

For the mechanical analyses of the axisymmetric structures in civil and mechanical engineering, combining the interpolating reproducing kernel particle method and the principle of minimum potential energy of space axisymmetrical elastic problems, the interpolating particle method for space axisymmetrical problem of elasticty is presented. And the corresponding matrix equations are deduced. This method employs the shape function with interpolating properties of scatter points and forms the displacement trial function to get rid of dependence on meshes, so it has an advantage that it can directly exert boundary conditions and can increase the computation efficiency. This method can obtain the global continuous stress field directly and avoid the fitting calculation error of stress in the post-processing of finite element method, then it is a high-precision numerical simulation method. Numerical examples are given to show the validity of the new mesh-less method in the paper.

Keywords:

作者及机构信息

1.
太原理工大学建筑与土木工程学院, 太原 030024;

2.
太原科技大学机械工程学院, 太原 030024;

3.
山推工程机械有限公司, 济宁 272000

基金项目: 国家自然科学基金(批准号: 51478290)和山西省自然科学基金(批准号: 2013011022-6)资助的课题.

Authors and contacts

1.
College of Architecture and Civil Engineering, Taiyuan University of Technology, Taiyuan 030024, China;

2.
College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China;

3.
Shantui Construction Machinery Co., Ltd, Shandong 272000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51478290) and the Natural Science Foundation of Shanxi Province, China (Grant No. 2013011022-6).

参考文献

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施引文献

[1]	Lancaster P, Salkauskas K 1981 Math. Comput. 37 141
[2]	Belytschko T, Lu Y Y, Gu L 1994 Int. J. Numer. Methods Engineer. 37 229
[3]	Cheng R J, Cheng Y M 2007 Acta Phys. Sin. 56 5569 (in Chinese) [程荣军, 程玉民 2007 56 5569]
[4]	Chen L, Cheng Y M 2010 Chin. Phys. B 19 090204
[5]	Cheng Y M, Peng M J 2005 Sci. China Ser G: Phys. Mech. Astron. 35 435 (in Chinese) [程玉民, 彭妙娟 2005 中国科学G: 物理学力学天文学 35 435]
[6]	Cheng R J, Ge H X 2009 Chin. Phys. B 18 4059
[7]	Cheng Y M, Liew K M, Kitipornchai S 2009 Int. J. Numer. Methods Engineer. 78 1258
[8]	Qin Y X, Cheng Y M 2008 Chin. J. Mech. Engineer. 44 95 (in Chinese) [秦义校, 程玉民 2008 机械工程学报 44 95]
[9]	Liu W K, Jun S, Zhang Y F 1995 Int. J. Numer. Methods Engineer. 20 1081
[10]	Liu W K, Chen Y, Uras R A, Chang C T 1996 Comput. Methods Appl. Mech. Engrg. 139 91
[11]	Gingold R A, Monaghan J J 1977 Monthly Notices of the Royal Astronomical Society 181 375
[12]	Chen J S, Yoon S, Wang H P, Liu W K 2000 Comput. Methods. Appl. Mech. Engrg. 181 117
[13]	Chen J S, Han W, You Y, Meng X P 2003 Int. J. Numer. Methods Engineer. 56 935
[14]	Atluri S N, Zhu T 1998 Computat. Mech. 22 117
[15]	Atluri S N, Kim H G, Cho J Y 1999 Comput. Mech. 24 348
[16]	Qin Y X, Cheng Y M 2009 Chin. J. Theoret. Appl. Mech. 41 898 (in Chinese) [秦义校, 程玉民 2009 力学学报 41 898]
[17]	Cheng Y M, Li J H 2006 Sci. China Ser. G: Phys. Mech. Astron. 49 46
[18]	Chen L, Cheng Y M 2010 Sci. China Ser. G: Phys. Mech. Astron. 53 954
[19]	Gao H F, Cheng Y M 2010 Int. J. Computat.Methods 7 55
[20]	Ren H P, Cheng Y M 2012 Engineer. Anal. Boundary Elements 36 873
[21]	Cheng Y M, Wang J F, Bai F N 2012 Chin. Phys. B 21 090203
[22]	Cheng Y M, Li R X, Peng M J 2012 Chin. Phys. B 21 090205
[23]	Cheng Y M, Wang J F, Li R X 2012 Int. J. Appl. Mech. 4 1250042
[24]	Wang J F, Cheng Y M 2013 Chin. Phys. B 22 030208
[25]	Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 57 6047]
[26]	Chen L, Cheng Y M 2010 Sci. China Ser. G: Phys. Mech. Astron. 40 242 (in Chinese) [陈丽, 程玉民 2010 中国科学G: 物理学力学天文学 40 242]
[27]	Weng Y J, Cheng Y M 2013 Chin. Phys. B 22 090204
[28]	He P X, Li Z R, Wu C C 2003 J. Univ. Sci. Technol. China 33 318 (in Chinese) [何沛祥, 李子然, 吴长春 2003 中国科技大学学报 33 318]
[29]	Li Z H, Qin Y X, Cui X C 2012 Acta Phys. Sin. 61 080205 (in Chinese) [李中华, 秦义校, 崔小朝 2012 61 080205]

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