文档介绍：第 26 卷第 2 期工程力学
2009 年 2 月 Feb. 2009 ENGINEERING MECHANICS 48
文章编号:1000-4750(2009)02-0048-05
有限深度 Gibson 地基上梁的稳定性
*刘齐建,赵跃宇,马建军
(湖南大学土木工程学院,湖南,长沙 410082)
摘要:采用变分原理,给出了地基弹性模量呈线性变化的 Gibson 地基上梁稳定性的解析方法。将非均匀地基
以改进 Vlasov 双参数模型模拟,并对地基-梁系统的最小势能取变分,得到梁稳定性计算的控制微分方程,然后
建立了特征参数γ与失稳模态的相关关系。梁的失稳荷载可通过求解特征值得到,采用简单的迭代程序可求得失
稳荷载与失稳模态。结果表明:地基土表层特性对地基模型的竖向弹性和连续特性影响较大,地基下部的影响有
限。地基非均匀性将影响梁的失稳荷载和失稳模态,上硬下软地基上梁失稳将需要更大的失稳荷载。
关键词:Gibson 地基;梁;稳定性;改进 Vlasov 模型;屈曲模态
中图分类号: 文献标识码:A
THE STABILITY OF BEAMS ON
ELASTIC LAYERED GIBSON FOUNDATION
*LIU Qi-jian , ZHAO Yue-yu , MA Jian-jun
(College of Civil Engineering, Hunan University, Changsha, Hunan 410082, China)
Abstract: An analytical method for the stability analysis of beams on the layered Gibson soil is developed. The
modified Vlasov model is adopted to simulate the foundation behavior. Using the variational principle, the
governing equation of the beam and the relation between parameter γ and buckling mode shape are derived. The
buckling loads and the corresponding mode shapes of the beam can be determined by solving the eigenvalues of
the boundary conditions of the beam. Parametric study shows that the soil properties near the surface have larger
influence on the vertical elasticity and continuity of the foundation than those near the bottom. The inhomogeneity
of the foundation affe