方波纹板和方形凹凸板等效刚度的解析公式  

Analytical solution of equivalent stiffness of square corrugated plate and square raised floor plate

作　　者：冯岩 杜国君[1] 赵卫东 高崇一[1] FENG Yan;DU Guojun;ZHAO Weidong;GAO Chongyi(Key Laborator^^of Mechanics Reliability for Heavy Equipment and Large Structure of Hebei Province,Yanshan University,Qinhuangdao,Hebei 066004,China)

机构地区：[1]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,河北秦皇岛066004

出　　处：《燕山大学学报》2018年第4期363-369,共7页Journal of Yanshan University

基　　金：河北省自然科学基金资助项目(E2017203115)

摘　　要：为了研究构造正交各向异方形凹凸板的等效刚度问题,应用Seydel的波纹板刚度计算公式和惯性矩求刚度法推导出方波纹板的弯曲刚度。在求得方波纹板弯曲刚度的基础上,考虑凹凸板的几何周期特性,将凹凸板划分为以凸起为中心的典型单元,先研究典型单元的刚度特性,再通过刚度组合方法得到了凹凸板的等效弯曲刚度。基于克希霍夫理论的正交构造异性板的小挠度弯曲方程,应用简支边矩形薄板的纳维解法,分别计算了在集中载荷作用下板的挠度和其自身的固有频率,与ANSYS有限元模拟结果进行对比,从而验证了所得等效刚度的精确性。除此之外讨论了方形凹凸板经典单元尺寸变化对其自身刚度的影响。本文给出的等效刚度解析方法便于工程应用,尤其在应对大规模凹凸板刚度求解中具有计算简便的优点。本研究结果可为凹凸板静动力学的研究发展以及实际工程应用提供参考。In order to research the equivalent stiffness of the structure of orthogonal anisotropic truss core panel,the bending stiffness of square corrugated panel is derived by the corrugated plate stiffness formulas of Seydel and the stiffness method of moment of inertia.Based on the theory of elastic thin plate and truss core panel geometry periodically,the plate is divided into typical element with the saddle-backing as a center.The stiffness characteristic of typical element is investigated,and the equivalent bending stiffness of truss core panel is obtained by the method of stiffness combination.Based on the Kirchhoff theory of the small deflection bending equation of orthotropic plate and the classical thin plate theory of Navier Dual Trigonometric Series promotion,the equation solution in this paper is compared with the ANSYS simulation results.And the rationality of equivalent stiffness is verified.Besides,the influence of the size change of the typical element on its own stiffness is discussed.The presented method is convenient for engineering application,especially in solving the large scale truss core panel computing.The present study refers to the development of static and dynamic mechanics about raised floor plate and application of actual engineering.

关 键 词：凹凸板 正交各向异性 方波纹板 刚度等效 有限元模拟 

分 类 号：O34[理学—固体力学]