Use of Layout Optimization to Solve Large-Scale Limit Analysis and Design Problems

Gilbert, Matthew; Smith, Colin C.; Hawksbee, Samuel; Tyas, A.

doi:10.1007/978-94-007-6827-7_8

Cited by 7 publications

(6 citation statements)

References 21 publications

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“…Considering Equations , and , the optimization formulation (written in matrix form) for the stability problem is obtained as follows:

\begin{matrix} array minimize & array \\ array & array \\ array E = e p, (F \cdot L) & array \\ array & array \\ array subject to & array \\ array & array \\ array [\begin{matrix} boldB & bold0 \\ boldN \\ boldG & bold0 \end{matrix}] [\begin{matrix} boldd \\ boldp \end{matrix}] = [\begin{matrix} bold0 \\ bold0 \\ 1 \end{matrix}], (\begin{matrix} sans-serif L \\ sans-serif L \\ sans-serif F \cdot sans-serif L \end{matrix}) & array \\ array & array \\ array and & array \\ array & array \\ array \{\begin{matrix} \forall i \in I_{s}, s_{i} = 0 \\ \forall i \in I_{n}, n_{i} = 0 \\ boldp \geq bold0 \end{matrix}, \end{matrix}

where I s and I n are respectively the sets of index of discontinuities fixed along the shear and normal directions. Equation is an LP problem, which presently can be efficiently solved on normal personal computers even with over millions unknowns …”

Section: Discontinuity Layout Optimizationmentioning

confidence: 99%

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Zhang

Zhuang

Lackner

2018

Num Anal Meth Geomechanics

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Summary For tunnel constructed by New Austrian Tunnelling Method, the crown is the upper part of tunnel section, constructed during excavation process and supported by shotcrete. The stability of the crown has great influence on the safety of tunnel itself and the buildings above, which correlates, among others, with geometrical setup of tunnel and material properties of shotcrete and soil/rock. In this paper, aiming at analyzing the stability of shotcrete supported crown, a recently presented numerical method discontinuity layout optimization is adopted, which introduces a great amount of potential discontinuities cross over one another and provides a wide search space for efficient upper limit analysis. In the analysis, a well‐established hydration model of cementitious material is implemented for accounting the hydration of shotcrete. Then assumptions based on convergence‐confinement method are used for accounting the 3‐dimensional effect in 2‐dimensional analysis, finally providing time‐space–dependent assessments of stability of shotcrete supported crown.

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“…Considering Equations , and , the optimization formulation (written in matrix form) for the stability problem is obtained as follows:

\begin{matrix} array minimize & array \\ array & array \\ array E = e p, (F \cdot L) & array \\ array & array \\ array subject to & array \\ array & array \\ array [\begin{matrix} boldB & bold0 \\ boldN \\ boldG & bold0 \end{matrix}] [\begin{matrix} boldd \\ boldp \end{matrix}] = [\begin{matrix} bold0 \\ bold0 \\ 1 \end{matrix}], (\begin{matrix} sans-serif L \\ sans-serif L \\ sans-serif F \cdot sans-serif L \end{matrix}) & array \\ array & array \\ array and & array \\ array & array \\ array \{\begin{matrix} \forall i \in I_{s}, s_{i} = 0 \\ \forall i \in I_{n}, n_{i} = 0 \\ boldp \geq bold0 \end{matrix}, \end{matrix}

Section: Discontinuity Layout Optimizationmentioning

confidence: 99%

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Zhang

Zhuang

Lackner

2018

Num Anal Meth Geomechanics

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“…Linear programming is also used in estimating the failure load of masonry made of rigid blocks considering non-associative friction [ 33 ]. The DLO has been subsequently applied to masonry wall [ 34 ], to retaining walls [ 35 ], in geotechnics [ 36 ], and to the yield-line method for slabs [ 37 ], and several examples of application to different civil engineering problems can be found in [ 38 ]. The computational efficiency of a discrete approach to layout optimization is shown in some recent papers [ 39 , 40 ].…”

Section: Introductionmentioning

confidence: 99%

Parametric Analysis of Failure Loads of Masonry Textures by Means of Discontinuity Layout Optimization (DLO)

2022

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Several masonry structures of cultural and historical interest are made with a non-periodic masonry material. In the case of periodic textures, several methods are available to estimate the strength of the masonry; however, in the case of non-periodic masonry, few methods are available, and they are frequently difficult to use. In the present paper we propose using discontinuity layout optimization (DLO) to estimate the failure load and mechanism of a masonry wall made with non-periodic texture. We developed a parametric analysis to account for the main features involved in the estimation of failure: in particular we considered three different textures (periodic, quasi-periodic, and chaotic), variable height-to-width ratio of the wall (from 0 to 3) and of the blocks (from 0.25 to 1), different mechanical properties of mortar joints and blocks, and possible presence of a load on the top. The results highlight the importance of the parameters considered in the analysis, both on the values of the failure load and on the failure mechanism. Therefore, it is found that DLO can be an useful and affordable method in order to assess the mechanical strength of masonry wall made with non-periodic textures.

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“…Given the development of modern optimization solvers, layout optimization problems with millions of unknowns can be solved efficiently. 3,4 The discontinuity layout optimization (DLO) method, first presented in Reference 5, optimizes the layout of discontinuities in a loaded structure. During optimization, DLO introduces millions of potential discontinuities that intersect with each other; the algorithm then seeks to minimize the dissipation energy of the system by optimizing the layout of these discontinuities.…”

Section: Introductionmentioning

confidence: 99%

Virtual displacement based discontinuity layout optimization

Zhang

Wang

et al. 2022

Numerical Meth Engineering

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Discontinuity layout optimization (DLO) is a relatively new upper bound limit analysis method. Compared to classic topology optimization methods, aimed at obtaining the optimum design of a structure by considering its self‐weight, building cost, or bearing capacity, DLO optimizes the failure pattern of the structure under specific loading conditions and constraints by minimizing the dissipation energy. In this work, we present a modified DLO algorithm that contains all of the advantages of DLO. It is referred to virtual displacement‐based discontinuity layout optimization (VDLO). VDLO takes the stress state of a loaded structure as a snapshot and correspondingly provides the optimum failure pattern, which greatly extends the application potential of DLO. Numerical examples indicate the effectiveness and flexibility of VDLO. It is regarded as a highly promising supplemental tool for other numerical methods in element‐/node‐based frameworks.

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Use of Layout Optimization to Solve Large-Scale Limit Analysis and Design Problems

Cited by 7 publications

References 21 publications

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Parametric Analysis of Failure Loads of Masonry Textures by Means of Discontinuity Layout Optimization (DLO)

Virtual displacement based discontinuity layout optimization

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