构造上正交各向异性半球形凸起凹凸板等效刚度研究  

Study on Equivalent Stiffnesses of Orthotropic Hemi-Spherical Convex Plates

作　　者：刘航 杜国君 冯岩 LIU Hang;DU Guojun;FENG Yan(Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structure of Hebei Province,School of Civil Engineering&Mechanics,Yanshan University,Qinhuangdao,Hebei 066004,P.R.China)

机构地区：[1]燕山大学建筑工程与力学学院河北省重型装备与大型结构力学可靠性重点实验室

出　　处：《应用数学和力学》2020年第1期70-80,共11页Applied Mathematics and Mechanics

摘　　要：根据半球形凹凸板周期性将其划分得到代表性体元结构.首先研究代表性体元的刚度特性,利用变形等效原理、均质化和刚度组合法得到半球形凹凸板的等效刚度.然后将得到的三个主向刚度代入四边简支板Navier解中求解板中心挠度.通过有限元数值模拟解和Navier解进行对比分析,从而验证该文得到的主向刚度的准确性.然后讨论了代表性体元的材料尺寸对所得等效刚度的影响.随着代表性体元边长与凸起半径的比值逐渐增大,所得结果精度越来越高,且等效刚度公式适用于不同厚度的半球形凹凸板.最后给出了较为简洁的工程应用公式,并给出了凸起半径的近似取值范围和工程应用算例.The hemispherical convex plate was periodically divided into representative unit structures.Firstly,the stiffness characteristics of representative units were studied,and the e-quivalent stiffness of the hemispherical convex plate was obtained by means of the deformation equivalence principle,the homogenization procedure and the stiffness combination method.Then the 3 principal stiffnesses were brought into the theoretical solution of the 4-side simple plate to solve the plate center deflection.The finite element numerical simulation solution and the theoretical solution were compared and analyzed to verify the accuracy of the theoretical principal stiffnesses.The effect of the material dimensions of the representative units on the e quivalent stiffness was then discussed.As the ratio of the length of the representative unit to the convex radius increases,the accuracy of the theoretical results will improve,and the equivalent stiffness formula is applicable to hemispherical convex plates of different thicknesses.Finally,a relatively simple engineering application formula was given with the approximate range of the convex radius based on several examples.

关 键 词：凹凸板 变形等效 代表性体元 刚度等效 有限元模拟 

分 类 号：O34[理学—固体力学]