考虑水平摩阻力的弹性地基梁大变形弯曲分析  

THE BENDING ANALYSIS OF A BEAM ON ELASTIC FOUNDATION WITH LARGE DEFLECTION INCLUDING THE EFFECTS OF HORIZONTAL FRICTION

作　　者：周慧[1] 罗松南[1] 孙丹[1] 

机构地区：[1]湖南大学力学与航空航天学院,湖南长沙410082

出　　处：《工程力学》2011年第1期43-47,54,共6页Engineering Mechanics

摘　　要：设水平摩阻力与垂直支承反力成正比,建立了任意对称荷载作用下有限长弹性地基梁大变形的平衡微分方程式。进行了合理的位移形函数假设,利用Galerkin方法建立非线性代数方程组,采用迭代法进行求解,得到了弹性地基梁的位移和内力解。通过实例计算可知,水平摩阻力对弹性地基梁的挠度和剪力影响很小,而对弯矩和轴力影响很大。当要考虑弹性地基梁的强度时,必须考虑水平摩阻力的影响。The equilibrium differential equations of finite long beams on an elastic foundation under an arbitrary symmetrical load were proposed on the basis of the horizontal friction being direct proportion to the supporting force.By utilizing the Galerkin integral method and adopting the model functions of displacements,the nonlinear algebraic equations are founded.Solving the nonlinear algebraic equations by an iterative method,the solutions of the internal force and displacements are obtained.By an example,it is founded that the horizontal friction has a less influence on the deflection and shearing force but it has a greatly influence on the bending moment and axial force of the beam.It is necessary that the horizontal friction is considered while strength of the beam on elastic foundation is analyzed.

关 键 词：弹性地基梁 水平摩阻力 大变形 挠度 内力 

分 类 号：TU471.2[建筑科学—结构工程]