基于厚板拉伸振动精确化方程求解动应力集中问题  

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

作　　者：胡超[1,2] 周传平[1] 佟广清[2] 刘殿魁[3] 

机构地区：[1]同济大学航空航天与力学学院,上海200092 [2]扬州大学建筑科学与工程学院,江苏扬州225127 [3]哈尔滨工程大学航天与建筑学院,哈尔滨150001

出　　处：《应用数学和力学》2013年第4期364-372,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10572045;51276129);航天创新科学研究基金资助项目

摘　　要：过去,对拉伸平板考虑应力集中的工程设计多借鉴弹性力学平面问题分析求解结果,例如弹性力学Kirsch问题的解或弹性动力学平面问题的解.基于厚板拉伸振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究.研究结果表明:1)两种模型得到的开孔附近的应力是不同的;2)当入射波波数变大或者说入射波频率变高时,动应力集中系数最大值趋于单位1.含孔平板拉伸振动的动应力集中系数最大值达到3.30,以及基于弹性动力学平面问题模型得到的结果为2.77.对数值计算结果做了分析讨论,可以看到,当孔径厚度比是a/h=0.10时,基于平板拉伸振动精确化方程得到的动应力集中系数可以达到最大值,超出基于弹性动力学平面问题所得到结果的19%.分析方法和数值计算结果可望能在工程平板结构的动力学分析和强度设计中得到应用.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 ex- ample, Kitsch＇ s solution and the solution of elastodynamics plane problems. Based on the refined dynamic equation of stretching plates, elastic wave scattering and dynamic stress concentradous in stretching plates with a circular cutout were studied. Numerical results demonstrated that dynamic stress concentration factors in stretching plates were different from the one 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 got by using plane problem of elastic dynamics is 2.77. The comparison of the numerical results was made and discussed. It is showed that as the cutout radius ratio to the thickness is a/h = 0. 10, using the refined equation the dynamic moment factor may approach the maximum value, which is 19% more than the result from the solution of plane problems of elastic dynamics. The results are more accurate because the refined equation of plate stretching is derivative without using any engineering hypoth- eses. The numerical results and the method can be used to analyze the dynamics and strength of plate-like structures.

关 键 词：平板拉伸振动精确化方程 弹性波散射与动应力集中 厚壁结构动力学 剪应力一阶矩 

分 类 号：O347.4[理学—固体力学] TU311.3[理学—力学]