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discontinuity layout optimization
Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load that can be carried by a solid or structure prior to collapse. Using DLO the layout of failure planes, or 'discontinuities', in a collapsing solid or structure are identified using mathematical optimization methods (hence the name, 'discontinuity layout optimization'). It is assumed that failure occurs in a ductile or 'plastic' manner.
==How it works==
The DLO procedure involves a number of steps, as outlined below.
The set of potential discontinuities can include discontinuities which crossover one another, allowing complex failure patterns to be identified (e.g. involving ‘fan’ mechanisms, where many discontinuities radiate from a point).
DLO can be formulated in terms of equilibrium relations ('static' formulation) or in terms of displacements ('kinematic' formulation). In the latter case the objective of the mathematical optimization problem is to minimize the internal energy dissipated along discontinuities, subject to nodal compatibility constraints. This can be solved using efficient linear programming techniques and, when combined with an algorithm originally developed for truss layout optimization problems,〔Gilbert, M. and Tyas, A. (2003) Layout optimization of large-scale pin-jointed frames, Engineering Computations, Vol. 20, No. 8, pp.1044-1064〕 it has been found that modern computer power can be used to directly search through very large numbers of different failure mechanism topologies (up to approx. 21,000,000,000 different topologies on current generation PCs). A full description of the application of DLO to plane strain problems has been provided by Smith and Gilbert,〔Smith, C.C. and Gilbert, M. (2007) Application of discontinuity layout optimization to plane plasticity problems, Proc. Royal Society A, Volume 463, Number 2086, pp.2461-2484.〕 to slab problems by Gilbert et al.〔Gilbert, M., He, L., Smith, C.C. and Le, C.V. (2014) Automatic yield-line analysis of slabs using discontinuity layout optimization. Proceedings Royal Society A, Volume 470, paper 20140071.〕 and to 3D problems by Hawksbee et al.〔Hawksbee, S., Smith, C.C. and Gilbert, M. (2013) Application of discontinuity layout optimization to three-dimensional plasticity problems. Proceedings Royal Society A, Volume 469, paper 20130009.〕
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