横观各向同性双参数地基上矩形薄板的弯曲  

The bending of rectangular thin plate on the transversely isotropic two-parameter elastic foundation

作　　者：何芳社[1] 悦峰 HE Fangshe;YUE Feng(School of Science,Xi′an Univ.of Arch.&Tech.,Xi′an 710055,China)

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）》2018年第5期755-760,共6页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(51178387)

摘　　要：弹性地基板是建筑工程中常见的构件,对其进行分析具有重要意义.对于工程中的大量由沉积作用形成的天然地基和分层碾压填筑而成的人工地基,采用横观各向同性地基模型更接近工程实际地基.本文将地基—板作为一个整体系统,利用最小势能原理,经过变分运算,推导建立了横观各向同性双参数弹性地基上矩形薄板弯曲的控制方程及其相应的边界条件.然后选取合理的挠度试函数,采用里兹法,对受横向荷载作用的四边自由矩形薄板进行了数值分析.计算表明:通过与其他文献的结果对比,两者吻合良好.所用理论在研究地基板的相互作用中具有普适性,为横观各向同性双参数弹性地基的应用奠定了基础.The plate on elastic foundation is the common structural component,so it is very important to have a detailed analysis about this plate for researchers.The transversely isotropic body will be more reasonable due to the experimental evidence for the large number of natural foundations formed by sedimentation and artificial foundations formed by stratifying and rolling in the project.The article completed the basic theory of plates by the principle of minimal potential energy and the variational calculus with the foundation and the plate as a whole system.The governing equations and the boundary conditions of plates on the bi-parameter foundations are given.The displacement function for meeting the correct boundary condition is selected.Ritz method is used to analyze the bending of plate,giving the deflection for the bending of rectangular plate with four free edges under lateral loads.In the end,the numerical calculations are accomplished.And compared to other literature,their results are coincident.The theory has some universality for analyzing the interaction between plate and elastic foundation.The method lays the foundation for the application of the transversely isotropic two-parameter elastic foundation.

关 键 词：横观各向同性 双参数地基 最小势能原理 矩形薄板 里兹法 

分 类 号：TU348[建筑科学—结构工程]