弹性基上圆柱管弯曲行为的高阶剪切梁理论解  

Theoretical solution of high-order shear deformation beam theory for bending behavior of cylindrical tube on elastic foundation

作　　者：马维力 申柳雷 宋殿义[2] 李显方[3] MA Weili;SHEN Liulei;SONG Dianyi;LI Xianfang(School of Sciences, Chang′an University, Xi′an 710064, China;College of Military Basic Education, National University of Defense Technology, Changsha 410072, China;School of Civil Engineering, Central South University, Changsha 410075, China)

机构地区：[1]长安大学理学院,陕西西安710064 [2]国防科技大学军事基础教育学院,湖南长沙410072 [3]中南大学土木工程学院,湖南长沙410075

出　　处：《国防科技大学学报》2022年第2期203-210,共8页Journal of National University of Defense Technology

基　　金：湖南自然科学基金资助项目(2021JJ30776)。

摘　　要：以弹性基上圆柱管为研究对象,基于高阶剪切变形梁理论推导了Winkler弹性基圆柱管弯曲变形的高阶剪切梁理论控制方程,给出四种典型工况弯曲问题的精确解。研究表明,无须假设剪切修正系数,只需引入适当横截面翘曲形状函数,高阶梁理论在圆柱管内外表面满足剪应力τ_(xr)为零的边界条件,且对于不同长径比和厚径比的圆柱管弯曲问题均能提供足够精度的解析解。弹性基刚度系数趋近于零时,圆柱管挠度曲线趋近于无弹性基圆柱管挠度曲线,验证了关于Winkler弹性基圆柱管弯曲问题求解方法的正确性。不同于Euler-Bernoulli梁理论,此方法的横截面上正应力不再与中性面上的横向坐标呈线性关系,且当长径比较小和厚径比较大时尤为明显。剪应力τ_(xz)在远离中性面时,应力值逐渐减小,在中性面的内表面处达到最大,在靠近顶部和底部位置时逐渐消失为零。The transverse bending of cylindrical tubes embedded in Winkler elastic foundation was studied based on the higher-order shear deformation beam theory.A governing equation for bending of circular cylindrical tubes on elastic foundation or in a surrounding Winkler matrix was derived and accurate solutions were presented for four typical boundary conditions.The obtained results show that the shear stress τ_(xr) automatically vanishes on the inner and outer surface of cylindrical tubes when an appropriate warping shape function instead of the shear correction coefficient is chosen.And it can provide analytical solutions with sufficient accuracy for the bending problems of cylindrical tubes with different length-diameter ratios and thickness-diameter ratios.When the stiffness coefficient approaches zero,the deflection curve of cylindrical tube embedded in Winkler elastic foundation approaches the deflection curve of cylindrical tube placed in free space,which verifies the accuracy of the present method.Different from the Euler-Bernoulli beam theory,the normal stress over the cross-section is no longer linear with the abscissa from the neutral surface in this method,and it is especially obvious when the length-diameter ratio is small and the thickness-diameter ratio is large.The shear stress τ_(xz) decreases when the distance from the neutral surface becomes large,approaching zero at the top and bottom positions,and the maximum shear stress occurs at the neutral surface which is close to the inner surface.

关 键 词：Winkler弹性基 圆柱管 高阶剪切变形梁理论 弯曲 

分 类 号：O343[理学—固体力学]