极限分析有限元法讲座Ⅲ——增量加载有限元法求解地基极限承载力

Analysis of ultimate bearing capacity of foundations by elastoplastic FEM through step loading

利用有限元法,通过增量加载的方式来求解地基极限承载力。随着荷载的逐渐增加,地基由初始的线性弹性状态逐渐过渡到塑性流动的极限破坏状态,此时有限元的计算将不收敛。它不但可以获得地基的极限荷载的值及荷载-位移关系,而且还能得到经典极限分析法中所采用到的破坏机构。当采用关联流动法则或采用剪胀角为 φ/2 的非关联流动法则时,获得的破坏机构与 Prandtl 的破坏机构一样。对 Prandtl 解的经典算例进行了分析,结果表明:屈服准则的选用对计算结果的影响很大,选择与实际问题相匹配的屈服准则方能得到比较精确的结果。在求解平面应变问题时,在关联流动法则条件下,采用Mohr-Coulomb 内切圆屈服准则,或在非关联流动法则下采用 Mohr-Coulomb 匹配 DP 准则所得结果与 Prandtl 精确解极为接近,可望应用于实际工程分析中。

The ultimate bearing capacity of foundations is analyzed by elastoplastic FEM through step loading. As the loads increase, the foundation status changes from elasticity to plasticity gradually, and finally the numerical non-convergence occurs. The solution of a classical Prandtl example shows that different yield criterions affect the results greatly; and only the use of the proper yield criterion can lead to the precise results. Under plane strain condition, the best solution can be obtained while Mohr-Coulomb inside-tangent circle yield criterion and associated flow rule, or Mohr-Coulomb matched D-P yield criterion and associated flow rule are used; and it can be applied to the analysis of practical engineering.