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中文摘要：
考虑非关联流动法则以及各向同性硬化条件，采用广义中点法（Generalized Midpoint Method，GMM）进行Dmcker-Prager（DP）弹塑性本构关系数值积分，给出调整后最终应力的解析解。GMM属于隐式算法，具有良好的计算精度与数值稳定性；最近点投影法（Closest Point Project Method，CPPM）是其特例，具有一阶精度并且无条件稳定。DP塑性势函数的特殊性质导致上述GMM解由初始应力状态与应变增量显式确定，无需迭代求解，因此计算效率大幅提高，同时避免了迭代过程的收敛性问题。数值算例证明：当加载偏离角度较大时，GMM（ξ=1／2）的计算精度高于CPPM，可适应更大的加载步长；而对于比例加载，任意GMM等同于精确解，采用CPPM可获得最高的计算效率。推导了满足DP屈服准则厚壁圆筒的弹塑性理论解，对比验证算法精度。采用非关联流动各向周性线性硬化DP材料模拟厚壁圆筒变形局部化效应。
英文摘要：
We present an analytical solution for the integration of Drucker-Prager （DP） elastic-plastic model considering non-associated flow rule and isotropic hardening using the Generalized Midpoint Method （GMM）. GMM is an implicit algorithm with good accuracy and stability, of which the Closest Point Project Method （CPPM） is a special case with first-order accuracy and unconditional stability. This GMM solution is an explicit function of the initial stress state and the strain increment due to the special characteristic of DP plastic potential function. Without any iterative process, the computational efficiency is greatly promoted and the convergence problem is naturally avoided. Numerical examples show the advantage in accuracy of GMM （ξ=-1/2） against CPPM when the deviation angle between the initial and incremental stress is large, but this advantage vanishes as the loading process approximates proportional. The theoretical solution of thick walled cylinder using DP yield criterion is derived to evaluate the accuracy of numerical solutions. The deformation localization effect of thickwalled cylinder is simulated using DP model with non-associated flow rule and isotropic linear hardening.
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