Discontinuity layout optimization

Discontinuity layout optimization (DLO) is an engineering analysis procedure which can be used to directly establish the amount of load required to cause a solid or structure to fail. Using DLO the layout of failure planes, or 'discontinuities', in a collapsing solid or structure are identified using mathematical optimization methods. It is assumed that failure occurs in a ductile or ' plastic' manner. Modern computer power can be used to directly search through huge numbers of different failure mechanism topologies (up to approx. 2^1000,000,000 different topologies on current generation PCs).

How it works

The DLO procedure involves a number steps, as outlined below (a coarse numerical discretization is shown for sake of clarity).

The potential discontinuities are free to crossover one another, giving a wide search space and allowing complex failure patterns to be identified (e.g. involving ‘fan’ mechanisms) to be identified without difficulty, and without the need to use tailored meshes etc. Also the problem posed can be solved using simple linear optimization techniques, ensuring that a globally optimal solution is obtainable. When the work method is used, the objective of the optimization is to minimize the internal energy dissipated along yield-lines, subject to nodal compatibility constraints.

DLO vs FEM

Whereas with finite element analysis, a widely used alternative engineering analysis procedure, mathematical relations are formed for the underlying continuum mechanics problem, DLO involves analysis of a potentially much simpler discontinuum problem, with the problem being posed entirely in terms of the individual discontinuities which interconnect nodes laid out across the body under consideration. Additionally, when general purpose finite element programs are used to analyse the collapse state often relatively complex non-linear solvers are required, in contrast to the simpler linear programming solvers often required with DLO.

Advantages and Disadvantages of Discontinuity Layout Optimization

Advantages

• Direct analysis of the collapse state
• Problems involving singularities in the stress or displacement fields can be dealt with without difficulty

Disadvantages

• DLO provides no information about displacements prior to collapse
• Relatively immature technique so limited range of DLO-based software available

Software using Discontinuity Layout Optimization

• MATLAB script
• LimitState:GEO software

External links

• cmd.sheffield.ac.uk