Winkler地基上边坡锚固框架设计计算的简明有限差分法

A Concise Finite Difference Method for Calculation of Slope Anchor Frame on Winkler Foundation

为克服现有Winkler地基上边坡锚固框架设计计算的有限差分法需假设框架在锚杆处截断的问题,通过建立受集中荷载作用的Winkler地基梁的挠曲微分方程,提出无需做截断处理的简明有限差分法。基于提出的差分方法,改进锚杆拉力在框架纵横梁上的分配与调整方法,并采用Matlab开发功能完善的程序。结果表明:有限差分数值解具有较高的计算精度,框架外伸段直接计算结果会出现负的土抗力,致使计算结果偏于不安全,可通过调整该段边界条件的方法予以消除,使最终计算结果更加可靠。本研究开发的差分程序对锚固框架整体设计提供了一种高效的计算方法。

The existing finite difference methods for the design calculation of slope anchor frames resting on the Winkler foundation is based on the assumption of cutting off the beams at the positions of anchor bolts,resulting in the complexity of derivation.For that,a concise finite difference method without the truncation treatment was proposed by establishing the flexural differential equation of the Winkler foundation beam subjected to concentrated loads.Additionally,the share and adjustment method of the tensile force on the vertical and transverse beams was modified based on the proposed finite difference method.A computation program with perfect function was then developed using the Matlab program language.The computation results of the examples show that the proposed finite element method is of very high precision.In the meantime,it found that even though the share and adjustment methods of the load at an intersection node in the existing textbooks are on the basis of the two conditionscompatible deformation and static equilibrium,the actual results cannot meet them well.In addition,negative soil resistances may occur in the direct computation results of the overhanging segments of a frame,leading to a computation result biased towards unsafety.They can be removed using the modified adjustment method to allow the results to be more reliable.Therefore,the proposed method perfectly solves the existing problems in the current approaches.