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系统地介绍了塑性极限分析上限法的原理和方法。根据上限法的基本原理,建立以内能耗散最小为目标函数,以结点速度及塑性乘子率为未知量的线性规划模型,并运用惩罚函数内点法求解极限承载力。在极限分析上限模型的基础上,求解地基极限承载力因数,讨论了屈服条件近似和网格划分对求解精度及时间的影响。对不同摩擦角下的承载力因数求解并与普朗特因数进行比较。算例表明该方法正确性且具有较高的精度。
The principle and method of plastic limit analysis method are systematically introduced. According to the basic principle of the upper bound method, the linear programming model with the minimum energy dissipation as the objective function and the node velocity and the plastic multiplier as the unknowns is established, and the ultimate bearing capacity is solved by the interior function of the penalty function. Based on the upper limit analysis model, the ultimate bearing capacity factor of the foundation is solved, and the influence of approximate yield conditions and meshing on the accuracy and time of the solution is discussed. The bearing capacity factors at different friction angles were solved and compared with the Prandtl number. The example shows that the method is correct and has high precision.