Topic
Discontinuity layout optimization
About: Discontinuity layout optimization is a research topic. Over the lifetime, 126 publications have been published within this topic receiving 2802 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, a technique for computing lower bound limit loads in soil mechanics under conditions of plane strain is described, where a perfectly plastic soil model is assumed, which may be either purely cohesive or cohesive-frictional, together with an associated flow rule.
Abstract: This paper describes a technique for computing lower bound limit loads in soil mechanics under conditions of plane strain. In order to invoke the lower bound theorem of classical plasticity theory, a perfectly plastic soil model is assumed, which may be either purely cohesive or cohesive-frictional, together with an associated flow rule. Using a suitable linear approximation of the yield surface, the procedure computes a statically admissible stress field via finite elements and linear programming. The stress field is modelled using linear 3-noded traingles and statically admissible stress discontinuities may occur at the edges of each triangle. Imposition of the stress-boundary, equilibrium and yield conditions leads to an expression for the collapse load which is maximized subject to a set of linear constraints on the nodal stresses. Since all of the requirements for a statically admissible solution are satisfied exactly (except for small round-off errors in the optimization computations), the solution obtained is a strict lower bound on the true collapse load and is therefore ‘safe’.
A major drawback of the technique, as first described by Lysmer,1 is the large amount of computer time required to solve the linear programming problem. This paper shows that this limitation may be avoided by using an active set algorithm, rather than the traditional simplex or revised simplex strategies, to solve the resulting optimization problem. This is due to the nature of the constraint matrix, which is always very sparse and typically has many more rows that columns. It also proved that the procedure can, without modification, be used to derive strict lower bounds for a purely cohesive soil which has increasing strength with depth. This important class of problem is difficult to tackle using conventional methods. A number of examples are given to illustrate the effectiveness of the procedure.
706 citations
TL;DR: In this article, a new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described, which is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems.
Abstract: A new and potentially widely applicable numerical analysis procedure for continuum mechanics problems is described The procedure is used here to determine the critical layout of discontinuities and associated upper-bound limit load for plane plasticity problems Potential discontinuities, which interlink nodes laid out over the body under consideration, are permitted to crossover one another giving a much wider search space than when such discontinuities are located only at the edges of finite elements of fixed topology Highly efficient linear programming solvers can be employed when certain popular failure criteria are specified (eg Tresca or Mohr–Coulomb in plane strain) Stress/velocity singularities are automatically identified and visual interpretation of the output is straightforward The procedure, coined ‘discontinuity layout optimization’ (DLO), is related to that used to identify the optimum layout of bars in trusses, with discontinuities (eg slip-lines) in a translational failure mechanism corresponding to bars in an optimum truss Hence, a recently developed adaptive nodal connection strategy developed for truss layout optimization problems can advantageously be applied here The procedure is used to identify critical translational failure mechanisms for selected metal forming and soil mechanics problems Close agreement with the exact analytical solutions is obtained
203 citations
TL;DR: Adaptive techniques, which decrease the number of optimization variables and lead to smooth results, are introduced and can be directly joined to conventional shape optimization.
Abstract: Topology optimization of continuum structures is often reduced to a material distribution problem. Up to now this optimization problem has been solved following a rigid scheme. A design space is parametrized by design patches, which are fixed during the optimization process and are identical to the finite element discretization. The structural layout is determined, whether or not there is material in the design patches. Since many design patches are necessary to describe approximately the structural layout, this procedure leads to a large number of optimization variables. Furthermore, due to a lack of clearness and smoothness, the results obtained can often only be used as a conceptual design idea. To overcome these shortcomings adaptive techniques, which decrease the number of optimization variables and generate smooth results, are introduced. First, the use of pure mesh refinement in topology optimization is discussed. Since this technique still leads to unsatisfactory results, a new method is proposed that adapts the effective design space of each design cycle to the present material distribution. Since the effective design space is approximated by cubic or Bezier splines, this procedure does not only decrease the number of design variables and lead to smooth results, but can be directly joined to conventional shape optimization. With examples for maximum stiffness problems of elastic structures the quality of the proposed techniques is demonstrated.
197 citations
TL;DR: In this paper, a simple but effective solution method capable of tackling problems with large numbers of potential members (e.g. >100,000,000) is presented. But this method requires a ground structure with minimal connectivity to be used in the first iteration; members are then added as required in subsequent iterations until the (provably) optimal solution is found.
Abstract: Computerized layout (or “topology”) optimization was pioneered almost four decades back. However, despite dramatic increases in available computer power and the application of increasingly efficient optimization algorithms, even now only relatively modest sized problems can be tackled using the traditional “ground structure” approach. This is because of the need, in general, for the latter to contain every conceivable member connecting together the nodes in a problem. A simple, but effective solution method capable of tackling problems with large numbers of potential members (e.g. >100,000,000) is presented. Though the method draws on the linear programming technique of “column generation”, since layout optimization specific heuristics are employed it is presented as an iterative “member adding” method. The method requires a ground structure with minimal connectivity to be used in the first iteration; members are then added as required in subsequent iterations until the (provably) optimal solution is found.
183 citations
TL;DR: In this paper, the authors give a realistic formulation of the filling problem that arises in layout optimization for manufacturability, and present efficient algorithms for density analysis, notably a multilevel approach that affords user-tunable accuracy.
Abstract: In very deep-submicron very large scale integration (VLSI), manufacturing steps involving chemical-mechanical polishing (CMP) have varying effects on device and interconnect features, depending on local characteristics of the layout. To reduce manufacturing variation due to CMP and to improve performance predictability and yield, the layout must be made uniform with respect to certain density criteria, by inserting "fill" geometries into the layout. To date, only foundries and special mask data processing tools perform layout post-processing for density control. In the future, better convergence of performance verification flows will depend on such layout manipulations being embedded within the layout synthesis (place-and-route) flow. In this paper, we give the first realistic formulation of the filling problem that arises in layout optimization for manufacturability. Our formulation seeks to add features to a given process layer, such that (1) feature area densities satisfy prescribed upper and lower bounds in all windows of given size and (2) the maximum variation of such densities over all possible window positions in the layout is minimized. We present efficient algorithms for density analysis, notably a multilevel approach that affords user-tunable accuracy. We also develop exact solutions to the problem of fill synthesis, based on a linear programming approach. These include a linear programming (LP) formulation for the fixed-dissection regime (where density bounds are imposed on a predetermined set of windows in the layout) and an LP formulation that is automatically generated by our multilevel density analysis. We briefly review criteria for fill pattern synthesis, and the paper then concludes with computational results and directions for future research.
114 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 4 |
| 2019 | 11 |
| 2018 | 6 |
| 2017 | 7 |
| 2016 | 6 |