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数值流形方法采用动态松弛法求解准静力学问题,能量耗散机制不清楚。通过引入黏性和自适应两种阻尼吸收系统产生的动能,基于最小势能原理建立了考虑阻尼力影响的总体平衡方程。提出了模拟岩体分期开挖的数值流形方法,将开挖面视为特殊的不连续面,根据开挖时序设置开挖面上接触点的状态,以达到模拟分步开挖的目的,给出了相应的迭代计算格式,并定义了位移和加速度收敛准则用以判断计算过程中系统是否达到新的平衡状态。数值算例结果表明,改进后的数值流形方法具有良好的收敛性能,其计算结果与解析解以及离散元是吻合的。
The numerical manifold method uses the dynamic relaxation method to solve quasi-static problems, and the energy dissipation mechanism is not clear. By introducing the kinetic energy produced by viscous and adaptive two kinds of damping absorption systems, an overall equilibrium equation considering the influence of damping force is established based on the principle of minimum potential energy. A numerical manifold method to simulate the staged excavation of rock mass is proposed. The excavation surface is regarded as a special discontinuity, and the state of the contact points on the excavation surface is set according to the excavation sequence so as to achieve the purpose of simulating step excavation. The corresponding iterative calculation format is given and the displacement and acceleration convergence criteria are defined to determine whether the system reaches a new equilibrium state during the calculation. Numerical examples show that the improved numerical manifold method has good convergence performance, and its calculation results are consistent with analytic solutions and discrete elements.