Zhang Yiming
Material-Technology Innsbruck (MTI) University of Innsbruck Technikerstraße 13 Innsbruck 6020 Austria.
Int J Numer Anal Methods Geomech. 2017 Mar;41(4):488-507. doi: 10.1002/nag.2566. Epub 2016 Aug 17.
Discontinuity layout optimization (DLO) is a recently presented topology optimization method for determining the critical layout of discontinuities and the associated upper bound limit load for plane two-dimensional and three-dimensional (3D) problems. The modelling process (pre-processing) for DLO includes defining the discontinuities inside a specified domain and building the target function and the global constraint matrix for the optimization solver, which has great influence on the the efficiency of the computation processes and the reliability of the final results. This paper focuses on efficient and reliable pre-processing of the discontinuities within the 3D DLO and presents a multi-slicing strategy, which naturally avoids the overlapping and crossing of different discontinuities. Furthermore, the formulation of the 3D discontinuity considering a shape of an arbitrary convex polygon is introduced, permitting the efficient assembly of the global constraint matrix. The proposed method eliminates unnecessary discontinuities in 3D DLO, making it possible to apply 3D DLO for solving large-scale engineering problems such as those involving landslides. Numerical examples including a footing test, a 3D landslide and a punch indentation are considered, illustrating the effectiveness of the presented method. © 2016 The Authors. International published by John Wiley & Sons Ltd.
间断布局优化（DLO）是一种最近提出的拓扑优化方法，用于确定二维平面和三维（3D）问题中不连续处的关键布局以及相关的上限极限载荷。DLO的建模过程（预处理）包括在指定域内定义不连续处，并为优化求解器构建目标函数和全局约束矩阵，这对计算过程的效率和最终结果的可靠性有很大影响。本文重点关注三维DLO中不连续处的高效可靠预处理，并提出了一种多切片策略，该策略自然地避免了不同不连续处的重叠和交叉。此外，引入了考虑任意凸多边形形状的三维不连续处的公式，使得全局约束矩阵的高效组装成为可能。所提出的方法消除了三维DLO中不必要的不连续处，使得将三维DLO应用于解决大规模工程问题（如涉及滑坡的问题）成为可能。考虑了包括基础测试、三维滑坡和冲压压痕在内的数值示例，说明了所提出方法的有效性。© 2016作者。由John Wiley & Sons Ltd国际出版。
