考虑水平力作用的弹性地基梁位移及内力解析解

An Analytical Solution of Beam on Elastic Foundation Subjected to Horizontal Force

考虑水平力作用下弹性地基梁受力特点,针对Winkler地基模型不能考虑梁底面间与地基切向相互作用的不足,在地基与梁体接触面上引入一系列各自独立的水平弹簧。假定弹簧反力与梁底和地基间的切向相对位移成正比,根据弹性力学基本原理,结合小变形条件下梁体几何方程和线弹性本构关系,建立力学分析模型,导出基本微分方程组并利用微分算子级数法进行求解,获得了考虑水平力作用时地基梁位移及内力解析解。最后通过实例分析,验证了该解析解的正确性和合理性,并对切向地基反力系数等影响因素进行了探讨。其结果可为工程设计提供借鉴参考。

Considering the bearing characteristics of beam on elastic foundation subjected to horizontal force,a series of horizontal springs are diverted to the face between beam bottom and foundation for surmounting the shortage of Winkler foundation model which ignores the tangential interaction between the beam and foundation.The horizontal spring reaction are assumed to be proportional to the relative tangential displacement.As the geometric equation and linear-elastic constitutive equation of beam have been presented based on the basic principle of elasticity mechanics,the analysis model is built and the governing differential equations about normal and tangential deflections of beam in small defromation condition are derived.The differential equations are solved by using differentiator series method with the help of boundary and continuity conditions,the analytical solutions of displacement and internal forces of beam on elastic foundation subjected to horizontal force are deduced.At last,on the base of examples,the validity and rationality of analytical solution are verified and some influence parameters including the tangential reaction coefficient kx are discussed.The results can be used as reference for engineering design.