Stability analysis of blocky system structures based on discontinuity layout optimization technique
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摘要: 计算块体结构体系的极限荷载和确定其相应的临界破坏模式是实际工程中的一项重要任务。非连续面拓扑优化技术（DLO）基于严谨塑性理论的速度非连续面（能量耗散）和优化理论从大量的潜在非连续面集中确定非连续面的临界布局,从而构成临界破坏模式。DLO程序利用栅格点阵进行离散,节点间连线为潜在滑移面或速度跳跃的非连续面。相容性通过直接检验节点运动变量的线性方程来实现。最终的目标函数为速度变量的线性函数,依据所有非连续面的平动和转动总耗散能量建立。为提高计算效率,在传统基结构的基础上,提出考虑杆件激活和冗余删除的自适应节点连接算法。虽然优化解受离散节点初始位置的影响,但通过细分栅格节点,节点的确切位置将对优化解的影响相对较小。与相关文献的基准问题和算例进行比对,验证DLO方法的应用潜力。研究表明,改进的自适应节点连接算法,可应用处理常规的块体结构稳定性问题,不仅极大地提高了计算效率,而且避免数值计算的持续振荡。Abstract: Computing the collapse loads and identifying the associated mechanism of block assemblage structures is an important task in practical engineering. The discontinuity layout optimization (DLO) is proposed entirely based on velocity discontinuities with rigorous plasticity theory, which the optimization uses to determine the critical arrangement of the discontinuities from a large set of potential discontinuities. In DLO procedure, the initial problem is discretized using the nodes distributed across the body under consideration. The potential discontinuity lines or slip lines along which jumps in rate of displacement are created by linking each node to every other node. Compatibility can be straightforwardly checked at each node by a simple linear equation involving movement variables. Finally an objective function may be defined based on the total energy dissipated due to translation along all discontinuities, a linear function of the velocity variables. In order to improve the performance of the classical ground structure approach, the adaptive member refinement (adaptive nodal connection procedure) considers both deletion and addition of members in the iterative process. Although the solution will be influenced somewhat by the starting position of the nodes, when fine nodal refinement is used, the exact positions of individual nodes will have relatively little influence on the solution generated. The procedure is applied to the problems from the literature and also to new benchmark problems including masonry walls and jointed rock slopes so as to illustrate potentialities of the method. The results show that the proposed adaptive member refinement algorithm can deal with the stability analysis of practical blocky structures and avoid oscillating between two different solutions at successive iterations with the results that the optimization efficiency is improved significantly.
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