弹性半空间地基上中厚圆板的幂级数解法  

The method of power series for mid-thick round plate on the elastic half-space foundation

作　　者：曹继明[1] 黄义[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《西安建筑科技大学学报（自然科学版）》2007年第3期339-344,共6页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(56978003)

摘　　要：弹性半空间地基上中厚板是板壳结构与周围介质相互作用研究领域的一个重要组成部分,但是鉴于问题本身的复杂性,目前这方面的研究还较少.应用幂级数方法求解了弹性半空间地基上周边自由的中厚圆板受均布荷载作用的弯曲问题.分别假设板的挠度和地基反力为幂级数的形式,采用比较系数法导出了问题求解的基本线性方程组.幂级数的引入,大大简化了计算.文中给出了算例.并与经典的薄板结果做了比较,计算结果表明幂级数解法的有效性.仅取很少几项就能达到很好的精度.The mid-thick plate on the elastic half space foundation is an important part of the field of interaction between structure of plates-shells and the medium. For the complicacy of this problem, the research on this aspect is rarely available. In this paper, power series method is used to solve the bending problem of a mid-thick round plate on the elastic half space foundation with free edge by distribute force. The deflection and subgrade reaction is expressed in power series form, and the coupled equations for the problem are presented by coefficient comparison. Numerical example is given to prove the validity of the new method in solving the problem. Compared with the result of classical thin plates, the numerical results show that power series method is effective. Very good precision can be obtained selecting only a few of the i- tems.

关 键 词：弹性半空间 中厚圆板 幂级数解法 

分 类 号：TU339[建筑科学—结构工程]