均布荷载下四边简支蜂窝式空心板的解析解-工程力学.pdfVIP

第 26 卷第 8 期 Vol.26 No.8 工 程 力 学 2009 年 8 月 Aug. 2009 ENGINEERING MECHANICS 34 文章编号：1000-4750(2009)08-0034-05 均布荷载下四边简支蜂窝式空心板的解析解 1 * 2 3 程远兵 ， 程文瀼 ，党 纪 (1. 华北水利水电学院土木与交通学院，河南，郑州 450011 ；2. 东南大学土木工程学院，江苏，南京 210096 ； 3. 爱知工业大学，日本，丰田 4700392) 摘 要：根据弹性薄板小挠度理论，结合蜂窝式空心板的受力与构造特点，推导了四边简支的蜂窝式空心板在竖 向均布荷载作用下的平衡微分方程，提出了其弯曲刚度和扭曲刚度的计算公式。采用二阶正弦级数形式的挠度表 达式，求出了板挠度和弯矩的解析解。进行了数组算例的有限元验证分析，理论分析结果和有限元的算例对比表 明提出的理论方法可以准确地计算蜂窝式空心板的内力和变形。 关键词：现浇混凝土；蜂窝式空心板；弹性薄板；简支；解析解；有限元法 中图分类号：TU313.1; TU375.2 文献标识码：A ANALYTICAL SOLUTION OF CELLULAR HOLLOW PLATES SIMPLY SUPPORTED SUBJECTED TO UNIFORMLY DISTRIBUTED LOADS 1 * 2 3 CHENG Yuan-bing , CHENG Wen-rang , DANG Ji (1. School of Civil and Transportation Engineering, North China University of Water Conservancy and Electric Power, Zhengzhou, Henan 450011, China; 2. School of Civil Engineering, Southeast University, Nanjing, Jiangsu 210096, China; 3. Aichi Institute of Technology, Toyota 4700392, Japan) Abstract: Based on the small deformation theory of elastic thin plates, considering of the peculiar mechanical and geometrical properties of the simply supported cellular hollow plates under uniformly distributed loads, the differential equilibrium equations were derived. Calculation formulae for the flexural and torsional stiffness were presented. Using the 2nd order trigonometric series expression of deflection, the analytical solutions for the deflection and bending moment of the cellular hollow plates simply supported at four edges were given. Finite element elastic analysis using ANSYS performed was