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构造连续相容的塑性变形场是MSD法的关键所在,但塑性变形场难以构造并且无普遍适用的构造方法。本文通过弹性有限元实现了虚拟加载上限法,真正解决了MSD类方法变形场构造困难的问题。其可同时获得给定位移下的荷载及相应的速度场,并将传统塑性上限分析中耗时的最优化分析等效为迭代计算。应用弹性有限元虚拟加载上限法分析了二维水平受荷桩、条形基础及条形锚板这3个土力学的经典问题,其获得的荷载–位移曲线和弹塑性有限元分析结果一致,并且其极限承载力逼近公认的塑性解,验证了本文方法分析整个加载过程的有效性。通过分析加载过程中的速度场,发现本文方法都是从同一初始速度场开始随迭代逐渐演化,在极限位移加载量下迭代收敛后获得的速度场和最优塑性破坏机构相似。本文方法可用于研究一些塑性速度场难以构造的复杂问题。
It is the key of MSD method to construct a continuous and consistent plastic deformation field, but the plastic deformation field is difficult to construct and there is no universally applicable construction method. In this paper, the upper limit of virtual loading method is realized by the elastic finite element method, which realizes the problem that the deformation field of MSD method is difficult to construct. It can obtain the load and the corresponding velocity field at a given displacement at the same time, and the iterative calculation is equivalent to the optimization analysis of the time consuming in the traditional plastic capping analysis. The upper bound method of elastic finite element virtual loading is used to analyze the classical problems of three soil mechanics, such as two-dimensional horizontal piles, strip foundation and strip anchor plate. The obtained load-displacement curve is consistent with the results of elasto-plastic finite element analysis. And its ultimate bearing capacity approximates the accepted plasticity solution, which verifies the effectiveness of this method in analyzing the whole loading process. By analyzing the velocity field in the process of loading, it is found that the proposed method evolves gradually with the iteration from the same initial velocity field. The velocity field obtained after iterative convergence under the limit displacement loading is similar to that of the optimal plastic failure mechanism. The proposed method can be used to study the complex problems of some plastic velocity fields.