Abstract
SummaryDiscontinuity 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.
Highlights
Topology optimization is a type of mathematical approach for searching for the optimum material layout considering a given space
B is a sparse matrix with row number 2 np or 3 ne and column number 2 nd or 3 nd, with nd being the total number of discontinuities
! If discontinuity i is fixed along the shear direction: set si D 0 I ! If discontinuity i is fixed along the normal direction: set ni D 0 I ! p 0: As mentioned before, to save computing resources in 3D discontinuity layout optimization (DLO), nj D pj tan j is considered for every inner discontinuity j
Summary
Topology optimization is a type of mathematical approach for searching for the optimum material layout considering a given space. Introducing large numbers of potential discontinuities permitted to crossover one another in a given domain and specifying the loading and boundary conditions (live loads, dead loads and supports), DLO can automatically generate a set of activated discontinuities corresponding to the upper bound limit load. This method has been successfully used to determine the slip-line mechanisms of several geotechnical problems [7, 10, 11], the yield-line failure of slabs [12, 13], failure mechanisms of masonry structures [14] and of retaining walls in seismic conditions [15].
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