基于弹性有限元的虚拟加载上限分析方法

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。

Fictitious loading upper bound limit analysis approach based on elastic FEM

For the MSD method, the most crucial point is the construction of compatible and continuous plastic deformation fields. However, plastic deformation fields are difficult to be obtained, and there exists no universally applicable method for that task. A fictitious loading upper bound limit analysis approach is implemented by the elastic FEM, which practically overcomes the inconvenience of deformation field construction as a prior condition for the MSD method. The proposed method can simultaneously acquire the load and the corresponding velocity field under a prescribed displacement, and the time-consuming optimization process required in the traditional upper bound limit analysis is equivalently converted into iteration here. The proposed method is applied in analyzing the shaft of laterally loaded pile, strip foundation and deep anchor. Judged from the three classic cases in soil mechanics, the load-displacement curves obtained by the proposed method are generally consistent with those obtained by the elasto-plastic FEM, and the obtained ultimate bearing capacities are close to the acknowledged plastic solutions, validating the effectiveness of the proposed method in the entire loading process. Through analyzing the velocity fields in the loading process, the same initial velocity field is identified, which gradually transforms with iteration, and when the limit displacement is applied, it finally becomes to be similar to the plastic collapse mechanisms. The proposed method can be utilized to study complicated problems, whose plastic deformation mechanisms are not acquired yet.