Summary 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 Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.

中文翻译：

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三维不连续布局优化（3D DLO）的多切片策略

总结 不连续布局优化 (DLO) 是最近提出的拓扑优化方法，用于确定平面二维和三维 (3D) 问题的不连续关键布局和相关的上限载荷。DLO 的建模过程（预处理）包括定义指定域内的不连续性，构建目标函数和优化求解器的全局约束矩阵，这对计算过程的效率和计算过程的可靠性有很大影响。最终结果。本文着重于对 3D DLO 内的不连续性进行高效可靠的预处理，并提出了一种多切片策略，自然避免了不同不连续性的重叠和交叉。此外，引入了考虑任意凸多边形形状的 3D 不连续性的公式，允许有效组装全局约束矩阵。所提出的方法消除了 3D DLO 中不必要的不​​连续性，使得将 3D DLO 应用于解决大型工程问题（例如涉及滑坡的问题）成为可能。考虑了包括基础测试、3D 滑坡和冲孔压痕在内的数值示例，说明了所提出方法的有效性。© 2016 作者。John Wiley & Sons Ltd. 出版的 International Journal for Numerical and Analytical Methods in Geomechanics。使应用 3D DLO 解决大型工程问题（例如涉及滑坡的问题）成为可能。考虑了包括基础测试、3D 滑坡和冲孔压痕在内的数值示例，说明了所提出方法的有效性。© 2016 作者。John Wiley & Sons Ltd. 出版的 International Journal for Numerical and Analytical Methods in Geomechanics。使应用 3D DLO 解决大型工程问题（例如涉及滑坡的问题）成为可能。考虑了包括基础测试、3D 滑坡和冲孔压痕在内的数值示例，说明了所提出方法的有效性。© 2016 作者。John Wiley & Sons Ltd. 出版的 International Journal for Numerical and Analytical Methods in Geomechanics。