构造上正交各向异性半球形凸起凹凸板等效刚度研究

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.

Study on Equivalent Stiffnesses of Orthotropic Hemi-Spherical Convex Plates

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.