Time Integration in Discontinuous Deformation Analysis
Time Integration in Discontinuous Deformation Analysis
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DOI：
10.1061/(asce)0733-9399(2004)130:3(249
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发表时间：
2004-03
期刊：
影响因子：
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通讯作者：
David Doolin;N. Sitar
中科院分区：
文献类型：
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作者：
David Doolin;N. Sitar
不连续变形分析（DDA）是为计算裂隙岩体大变形而发展起来的一种离散元方法。在本文中，我们详细介绍了DDA时间积分方案，其中加速度在时间步长上取常数，等于时间步长结束时的加速度（“右黎曼”）。该积分方案具有以下几个优点：(1)自启动；(2)不需要计算加速度，从而降低了实现的复杂性；(3)无条件稳定；(4)耗散，包含算法阻尼，考虑到DDA的惩罚公式可能很重要。然而，正确的黎曼格式是隐式的，需要昂贵的因式分解或迭代来求解得到的方程组，并且当时间步长相对于周期较大时，谱中会出现分岔。这种分岔对于控制DDA仿真中由于系统线性标度引起的杂散共振具有重要意义。
Discontinuous deformation analysis (DDA) is a discrete element method that was developed for computing large deformation in fractured rock masses. In this paper we present details of the DDA time integration scheme, where the acceleration is taken constant over the time step, equal to the acceleration at the end of the time step (“right Riemann”). The integration scheme has several advantages: (1) Self-starting, (2) accelerations never need to be computed which reduces implementation complexity, (3) unconditionally stable, and (4) dissipative, contains algorithmic damping which may be important considering the penalty formulation of DDA. However, the right Riemann scheme is implicit, requiring expensive factorization or iteration to solve the resulting system of equations, and is accompanied by a bifurcation in the spectrum when the time step is large with respect to the period. This bifurcation has important ramifications for controlling spurious resonance in DDA simulations due to linear scaling in syst...