Dynamic stress concentrations in thick plates with two holes based on refined theory

doi:10.1007/s10483-014-1883-6

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (12): 1591-1606.doi: https://doi.org/10.1007/s10483-014-1883-6

Dynamic stress concentrations in thick plates with two holes based on refined theory

周传平¹, 胡超², F. MA³, 刘殿魁⁴

1. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, P. R. China;
2. College of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, Jiangsu Province, P. R. China;
3. College of Engineering, University of California, Berkeley 94720, U. S.A.;
4. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P. R. China

收稿日期:2013-10-17 修回日期:2014-05-07 出版日期:2014-12-01 发布日期:2014-12-01
通讯作者: Chao HU, Professor, Ph.D., E-mail: chaohu@yzu.edu.cn E-mail:chaohu@yzu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos.51378451 and 51378245)

Dynamic stress concentrations in thick plates with two holes based on refined theory

Chuan-ping ZHOU¹, Chao HU², F. MA³, Dian-kui LIU⁴

1. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou 310018, P. R. China;
2. College of Civil Science and Engineering, Yangzhou University, Yangzhou 225127, Jiangsu Province, P. R. China;
3. College of Engineering, University of California, Berkeley 94720, U. S.A.;
4. College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, P. R. China

Received:2013-10-17 Revised:2014-05-07 Online:2014-12-01 Published:2014-12-01
Contact: 10.1007/s10483-014-1883-6 E-mail:chaohu@yzu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.51378451 and 51378245)

摘要/Abstract

摘要： Based on complex variables and conformal mapping, the elastic wave scattering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonal function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concentration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

关键词: complex variable and conformal mapping method, elastic wave scattering and dynamic stress concentrations, thick plate, two holes, refined vibration equation

Abstract: Based on complex variables and conformal mapping, the elastic wave scattering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonal function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concentration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese.

Key words: refined vibration equation, thick plate, elastic wave scattering and dynamic stress concentrations, complex variable and conformal mapping method, two holes

中图分类号:

周传平;胡超;F. MA;刘殿魁. Dynamic stress concentrations in thick plates with two holes based on refined theory[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(12): 1591-1606.

Chuan-ping ZHOU;Chao HU;F. MA;Dian-kui LIU. Dynamic stress concentrations in thick plates with two holes based on refined theory[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(12): 1591-1606.

参考文献

[1] Savin, G. N. Stress Concentration Around Holes, Pergamon Press, Oxford (1961)
[2] Muskhelishvili, N. I. Some Basic Problems of the Mathematical Theory of Elasticity, Springer, Heidelberg, 188-189 (1977)
[3] Pao, Y. H. and Maw, C. C. Diffraction of Elastic Wave and Dynamic Stress Concentration, Crane and Russak, New York, 113-121 (1973)
[4] Liu, D. K. and Hu, C. Scattering of flexural wave and dynamic stress concentration in Mindlin thick plates. Acta Mechanica Sinica, 12, 169-185 (1996)
[5] Liu, D. K., Gai, B. Z., and Tao, G. Y. Applications of the method of complex functions to dynamic stress concentrations. Wave Motion, 4, 293-304 (1982)
[6] Pao, Y. H. Elastic wave in solids. Journal of Applied Mechanics, 50, 1152-1164 (1983)
[7] Bedford, A. and Drumheller, D. S. Introduction to Elastic Wave Propagation, Wiley, 162-166 (1994)
[8] Saada, A. S. Elasticity: Theory and Applications, J. Ross Pub., Fort Lauderdale, 147-163 (2009)
[9] Reissner, E. The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics, 12, 69-75 (1945)
[10] Mindlin, R. D. Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates. Journal of Applied Mechanics, 18, 31-36 (1951)
[11] Eringen, A. C. and Suhubi, E. S. Elastodynamics, Volume II, Linear Theory, Academic Press, New York, 112-126 (1975)
[12] Hu, C., Ma, F., Ma, X. R., and Huang, W. H. Refined dynamic equations of the plate bending without any assumptions (in Chinese). Scientia Sinica Physica, Mechanica and Astronomica, 41, 781-790 (2011)
[13] Hu, C., Ma, F., Ma, X. R., and Huang, W. H. Refined dynamic theory of thick plates and its new formulism (in Chinese). Scientia Sinica Physica, Mechanica and Astronomica, 42, 522-530 (2012)
[14] Hu, C., Zhou, C. P., Ma, F., and Liu, D. K. Dynamic stress concentrations by using the refined equation of plates (in Chinese). Chinese Journal of Theoretical and Applied Mechanics, 44, 938- 942 (2012)
[15] Hu, C., Zhou, C. P., Ni, B., and Liu, D. K. Dynamic stress concentrations in thick plates with an arbitrary cutout by using the refined theory (in Chinese). Chinese Journal of Solid Mechanics, 34, 410-416 (2013)

Dynamic stress concentrations in thick plates with two holes based on refined theory

Dynamic stress concentrations in thick plates with two holes based on refined theory

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 12

编辑推荐

Metrics

本文评价

[1]	张鹤;蒋吉清;张治成. Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1467-1478.
[2]	孙卫明;杨光松. RATIONAL FINITE ELEMENT METHOD FOR ELASTIC BENDING OF REISSNER PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1999, 19(2): 193-199.
[3]	尹益辉;陈刚;陈裕泽. A SOLVING METHOD FOR A SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS WITH AN APPLICATION TO THE BENDING PROBLEM OF A THICK PLATE[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(11): 1259-1265.
[4]	徐旭;何福保. THREE DIMENSIONAL ELASTICITY SOLUTION FOR VIBRATION PROBLEM OF THICK PLATE[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(7): 615-624.
[5]	肖万伸;曾庆元;刘庆潭. THREE-DIMENSIONAL ANALYSIS ON PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1997, 18(9): 891-903.
[6]	沈惠申;朱湘赓. THERMAL POSTBUCKLING ANALYSIS OF MODERATELY THICK PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(5): 475-484.
[7]	张音翼. FREE VIBRATION AND STABILITY OF MODERATE-THICK CANTILEVER PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(2): 161-167.
[8]	成振强;王秀喜;黄茂光. POSTBUCKLING BEHAViOR OF RECTANGULAR MODERATELYTHICK PLATES AND SANDWICH PLATES[J]. Applied Mathematics and Mechanics (English Edition), 1994, 15(7): 605-610.
[9]	唐寿高;袁驷. THE VIBRATION AND STABILITY ANALYSIS OF MODERATE THICK PLATES BY THE METHOD OF LINES[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(6): 523-531.
[10]	杨正文;杨挺青. AN EQUATION OF MOTION FOR A THICK VISCOELASTIC PLATE[J]. Applied Mathematics and Mechanics (English Edition), 1992, 13(5): 477-486.
[11]	纪振义. AN EXACT ELEMENT METHOD FOR THE BENDING OF NONHOMOGENEOUS REISSNER'S PLATE[J]. Applied Mathematics and Mechanics (English Edition), 1991, 12(11): 1065-1074.
[12]	汪克让. THICK RECTANGULAR PLATES WITH FREE EDGES ON ELASTIC FOUNDATIONS[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(9): 869-879.