弹性地基上无限大板的统一解  

The unified solution of infinite plate on elastic foundation

作　　者：谈至明[1] 郭晶晶[1] 

机构地区：[1]同济大学道路与交通工程教育部重点实验室,上海200092

出　　处：《应用力学学报》2016年第1期25-29,177,共5页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51378394)

摘　　要：利用汉克尔变换法,推演得到了文克勒地基、双参数地基、弹性半空间体地基上无限大薄板,赖斯纳、汉盖、克罗姆等中厚板,在任意竖向荷载作用下的统一解;并给出了竖向轴对称荷载条件下的无限大板挠度、弯矩、剪力系数、地基反力系数的计算公式;最后,对圆形均布荷载作用下的不同地基和板模型的板挠度和弯矩进行了对比分析。结果表明：半空间体地基板与文克勒地基板的荷载圆中点的弯矩参数十分相近,但其荷载圆中点挠度系数较后者大1/3~1/2;中厚板理论对地基板挠度有更好地拟合和解析,但对板弯矩等内力的计算精度无改善。Hankel transform method is used to get unified solution of infinite thin plate and medium thick plate including Reissener, Henky and Krommon Winkler foundations, double-parameter foundation and elastic half-space foundation under any vertical load. Then it presents calculation formula of infinite plate deflection, bending moment, shear force coefficient and the coefficient of subgrade reaction force on vertical axisymmetric load. At last, deflection and bending moment of different foundation and plate model under the action of the circular uniformly distributed load are analyzed and compared.

关 键 词：弹性地基板 汉克尔变换 文克勒地基 双参数地基 弹性半空间体地基 薄板 中厚板 

分 类 号：O343[理学—固体力学]