庄妍 王孟 王康宇

摘 要：为了研究移动荷载作用下结构的安定性问题，以Melan静力型安定定理为基础，通过构造满足静力平衡条件的最佳残余应力场，并求解移动荷载作用下结构中的真实弹性应力场，发展了一种弹塑性安定性计算方法.该方法摆脱了传统安定性分析方法中的数学规划运算，解决了计算中维数障碍的问题.通过与前人研究结果对比，说明本方法的正确性.基于此方法，研究了列车荷载直接作用下路基的静力安定极限的第一类上限kI和静力安定极限kSD，进行轮载间距L和铁轨间距B对路基安定极限的敏感性分析，发现当轮载间距L和铁轨间距B大于等于10a时，轮载间距L和铁轨间距B对路基安定极限不再产生影响；通过分析材料泊松比v和内摩擦角φ对安定极限的影响，表明安定极限随着路基泊松比的增大略有减小，但随着内摩擦角的增大而有明显增加；并提出了一种基于安定极限荷载包络图的路基安定性评价方法和设计方法，据此可对铁路路基进行设计指导和安全性评价.

关键词：安定分析；铁路；赫兹荷载；Melan静力安定定理；移动荷载；弹塑性材料

中图分类号：TU4 文献标志码：A

文章編号：1674—2974（2018）07—0093—10

Abstract： An elastic-plastic shakedown solution is established for the shadedown analysis of the structure under moving loads.On the basis of the Melans static shakedown theorem，this method is developed by searching for the best residual stress field，and calculating the actual elastic stress field subjected to the moving loads.This method avoids the operation of mathematical programming in traditional method of shakedown analysis，and therefore obstruction due to large scale mathematical programming is overcome. The validity of this method is verified by comparing the results of the previous study. Based on this method，the upper bound type 1 shakedown limit kI and static shakedown limit kSD of railway subgrade are presented. A sensitive analysis is also presented， showing that the shakedown limit remains stable if the distance between the loads L and rails B is longer than 10a，so that the upper bound type 1 shakedown limit kI is shown. Meanwhile， by means of investigation on the influence of Poisson′s ratio and internal friction angle， it is found that the static shakedown limit kSD diminish marginally with the increase of Poisson′s ratio， while both the upper bound type 1 shakedown limit kI and static shakedown limit kSD experience a steadily growth with the increase of internal friction angle. A design method for subgrade is finally proposed based on the envelope diagram of shakedown limits， which can provide guidelines for design and safety assessment of railway subgrade.

Key words： shakedown analysis；railways；Hertz load；Melan′s lower-bound shakedown theorem；moving load；elastis plastic materials

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