构造上正交各向异性半球形凸起凹凸板等效刚度研究

Abstract

The hemispherical convex plate was periodically divided into representative unit structures. Firstly, the stiffness characteristics of representative units were studied, and the equivalent 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 equivalent 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.