基于直接刚度法的弹性地基深梁单元  

Deep Beam Element on Elastic Foundation Based on Direct Stiffness Method

作　　者：丁敏[1] 李静[1,2] 罗双[1,3] 曹琼琼 DING Min;LI Jing;LUO Shuang;CAO Qiongqiong(College of Water Resources and Civil Engineering,China Agricultural University,Beijing 100083,China;Department of Environmental Art Engineering,Henan Polytechnic,Zhengzhou 450046,China;Department of Infrastructure,Chinese Academy of Agricultural Sciences,Beijing 100081,China;China Railway Service Co.,Ltd.,China Railway,Beijing 100844,China)

机构地区：[1]中国农业大学水利与土木工程学院,北京100083 [2]河南职业技术学院环境艺术工程学院,河南郑州450046 [3]中国农业科学院基本建设局,北京100081 [4]中国国家铁路集团有限公司铁总服务有限公司,北京100844

出　　处：《铁道学报》2020年第5期136-142,共7页Journal of the China Railway Society

基　　金：国家自然科学基金(11672362);农业部重点实验室开放课题(201502)。

摘　　要：为研究弹性地基深梁的受力及变形性能,根据双参数弹性地基模型和Timoshenko深梁模型的基本方程,建立了弹性地基深梁挠度控制方程,求得了挠度方程全解,并给出了弹性地基深梁梁轴转角、截面弯曲转角及剪切角的表达式;结合节点位移条件,得到了位移系数;根据节点力方程建立了刚度平衡方程,给出了弹性地基深梁的刚度矩阵方程及均布荷载的等效节点力向量。在此基础上,分别计算了均布荷载、跨中集中力、两端集中力、两端集中力矩等荷载工况下的节点位移,求得弹性地基深梁挠度曲线,验证了本文给出的刚度矩阵方程及等效节点力向量的合理性及适用性。In order to analyze the mechanical behavior and deformation performance of deep beam on elastic foundation,the deflection control equation of deep beam on elastic foundation was deduced on the basis of basic equations of double-parameter elastic foundation model and Timoshenko deep beam model,by which its full solution was obtained.The expressions for the beam axis angle,the section flexural angle and the shear angle of deep beam on elastic foundation were developed.Combined with the displacement boundary conditions,the displacement coefficient was received.According to the nodal force equations,the stiffness balance equation was established,while the stiffness matrix equation and equivalent nodal force vector under uniform load for deep beam on elastic foundation were provided.On this basis,the nodal displacement under the uniform load,the concentrated load at the mid-span,the concentrated force at both ends,and the concentrated moment at both ends were calculated,respectively,to obtain the deflection curve of deep beam on elastic foundation,which verified the rationality and applicability of stiffness matrix equation and equivalent nodal force vector in this paper.

关 键 词：直接刚度法 弹性地基梁 深梁单元 刚度矩阵 等效节点力 

分 类 号：TU348[建筑科学—结构工程]