Dynamic Stress Concentrations in Stretching Plates by Using the Refined Dynamic Theory

HU Chao; ZHOU Chuan-ping; TONG Guang-qing; LIU Dian-kui

doi:10.3879/j.issn.1000-0887.2013.04.005

Volume 34 Issue 4

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2013 > 34(4): 364-372

HU Chao, ZHOU Chuan-ping, TONG Guang-qing, LIU Dian-kui. Dynamic Stress Concentrations in Stretching Plates by Using the Refined Dynamic Theory[J]. Applied Mathematics and Mechanics, 2013, 34(4): 364-372. doi: 10.3879/j.issn.1000-0887.2013.04.005

Citation:

PDF( 1320 KB)

Dynamic Stress Concentrations in Stretching Plates by Using the Refined Dynamic Theory

doi: 10.3879/j.issn.1000-0887.2013.04.005

¹School of Aerospace Engineering and Applied Mechanics, Tongji University,Shanghai 200092, P.R.China;²SCollege of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu 225127, P.R.China;³SCollege of Aerospace and Civil Engineering, Harbin Engineering University, Harbi 150001, P.R.China

Received Date: 2013-01-07
Rev Recd Date: 2013-03-08
Publish Date: 2013-04-15

Abstract

Abstract

In the past, the solution of elasticity plane problems is often used to investigate stress concentrations for the engineering design instead of solution of stretching plates. For example, Kirsch’s solution and the solution of elastodynamics plane problems. Based on the refined dynamic equation of stretching plates, elastic wave scattering and dynamic stress concentrations in plates with a circular cutout were studied. Numerical results demonstrated that dynamic stress concentration factors in stretching plates were different from the one which were obtained by elasticity plane problems and dynamic stress concentration factors trended to unit 1 at the high frequency of incident waves. The dynamic stress concentration factor of stretching plates with cutouts is up to a maximum of 3.30, and the one is 2.77 by using plane problem of elastic dynamics. The comparison of the numerical results was made and discussed. It is showed that as the cutout radius ratio to the thickness is smaller a/h=0.10,using the refined equation the dynamic moment factor may approach to the maximum value, which is more 19% than the result from the solution of plane problems of elastic dynamics. The results are more accurate because the refined equation of plates stretching is derivative without using any engineering hypotheses. The numerical results and the method can be used to analyze the dynamics and strength of platelike structures.

FullText(HTML)

References(10)

References

[1]	萨文 Γ H.孔附近的应力集中[M]. 卢鼎霞译. 北京：科学出版社, 1965.（Savin E H.Stress Concentrations at the Edge of a Hole[M]. LU Ding-xia trans. Beijing: Science Press, 1965.（Chinese version））
[2]	Liu D K, Hu C. Scattering of flexural wave and dynamic stress concentration in Mindlin thick plates[J].Acta Mech Sin,1996, 12(2): 169-185.
[3]	Reissner E. The effect of transverse shear deformation on the bending of elastic plates[J].ASME, J Appl Mech,1945, 12(2):69-77.
[4]	Mindlin R D. Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates[J].ASME, J Appl Mech,1951, 18(2): 31-36.
[5]	Pao Y H, Mao C C. Diffractions of flexural waves by a cavity in an elastic plate[J].AIAA J,1964, 2(11): 2004-2010.
[6]	Vemula C, Norris A N. Flexural wave propagation and scattering on thin plates using Mindlin theory[J].Wave Motion,1997, 26(1): 1-12.
[7]	胡超, 周传平, Fai Ma, 刘殿魁.基于平板弯曲振动精确化方程求解动应力集中问题[J]. 力学学报, 2012, 44(5): 938-942.（HU Chao, ZHOU Chuan-ping, Fai Ma, LIU Dian-kui. Dynamic stress concentrations by using refined equations of plate bending[J].Chinese Journal of Theoretical and Applied Mechanics,2012, 44(5): 938-942. (in Chinese)）
[8]	Hwu C B. Boundary element formulation for the coupled stretchingbending analysis of thin laminated plates[J].Engineering Analysis With Boundary Elements,2012, 36(6): 1027-1039.
[9]	胡超, Fai Ma, 马兴瑞, 黄文虎. 厚板弯曲与拉伸振动精化理论及其求解新途径[J]. 中国科学,G辑, 物理、力学、天文学, 2012, 42(5): 522-530. （HU Chao, Fai Ma, MA Xing-rui, HUANG Wen-hu. Refined dynamic theory of thick plates and its new formulism[J].Sci China, ser G, Phys, Mech, Astron,2012, 42(5):522-530. (in Chinese)）
[10]	鲍亦兴, 毛昭宙. 弹性波的衍射与动应力集中[M]. 刘殿魁, 苏先樾译. 北京: 科学出版社, 1993: 230-231.（Pao Y H, Mao C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations [M]. LIU Dian-kui, SU Xian-yue trans. Beijing: Science Press, 1993: 230231. (Chinese version)）