Colin C. Smith

Application of discontinuity layout optimization to plane plasticity problems

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 (e.g. 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 (e.g. 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.

Physical modelling of solute transport in porous media: evaluation of an imaging technique using UV excited fluorescent dye.

The development and evaluation of a 2-dimensional physical model, which is designed to assist in the characterisation of complex solute transport problems in porous media, is described. The laboratory model is a transparent 2-dimensional porous media of nominal thickness and uses a non-invasive imaging technique in conjunction with a fluorescent dye tracer (sodium fluorescein) to monitor solute movements. Under ultraviolet (UV) illumination the dye emits visible light which is imaged by a CCD (Charge Coupled Device) camera. The image is processed to estimate the 2-dimensional distribution of tracer concentrations. The system can successfully model a simple contaminant plume within a homogenous porous matrix constructed from glass beads (60-100 microm). Experimental results show that transverse dispersion coefficient was 3.9 x 10(-10) m2/s when sodium fluorescein transported in porous matrix with a walter velocity of 5.71 x 10(-6) m/s. The low transverse dispersion coefficient suggests that the molecular diffusion of solute cannot be neglected under low velocity of the water. The advantages of using UV rather than an ordinary light system are a reduction in noise and experimental errors. Errors due to light dispersion within the model are shown to be negligible for the current model. Since contaminant with aromatic rings are usually fluorescent and biological samples can be labelled by fluorescent dye, this imaging technique using UV excited fluorescent dye will be used to investigate biodegradation process in porous media.

Limit loads for an anchor/trapdoor embedded in an associative coulomb soil

A methodology for determining the plane strain limit load acting on an anchor or trapdoor buried within a purely associative Coulomb soil is presented. True lower bounds derived from a family of limiting stress fields appropriate to shallow horizontal trapdoors and anchors are shown to correlate to within less than 1 percent of upper bounds available in the literature, permitting the true limit load to be almost exactly defined. The solution form alters for deeply buried anchors and trapdoors resulting in poorer correlations. Methods by which the work may be extended to cover the more practical instances of non-associative Coulomb soils are indicated but are beyond the scope of the current paper.

Automatic yield-line analysis of slabs using discontinuity layout optimization.

The yield-line method of analysis is a long established and extremely effective means of estimating the maximum load sustainable by a slab or plate. However, although numerous attempts to automate the process of directly identifying the critical pattern of yield-lines have been made over the past few decades, to date none has proved capable of reliably analysing slabs of arbitrary geometry. Here, it is demonstrated that the discontinuity layout optimization (DLO) procedure can successfully be applied to such problems. The procedure involves discretization of the problem using nodes inter-connected by potential yield-line discontinuities, with the critical layout of these then identified using linear programming. The procedure is applied to various benchmark problems, demonstrating that highly accurate solutions can be obtained, and showing that DLO provides a truly systematic means of directly and reliably automatically identifying yield-line patterns. Finally, since the critical yield-line patterns for many problems are found to be quite complex in form, a means of automatically simplifying these is presented.

Application of discontinuity layout optimization to three-dimensional plasticity problems

A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr–Coulomb yield criteria. This allows traditional ‘upper bound’ translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.

Ultimate Limit State Design to Eurocode 7 using numerical methods

Summary Assessment of the Ultimate Limit State (ULS) in Eurocode 7 is to be carried out using “Design Approach 1” in the UK. In most cases this involves two design checks, one which primarily involves an “action factor” approach (Design Approach 1, Combination 1, termed DA1/1) and one which primarily involves a “material factor” approach (Design Approach 1, Combination 2, termed DA1/2). The latter is generally straightforward to implement in numerical analysis procedures, but the former is potentially more challenging. A survey of the current literature on Eurocode 7 indicates differences of opinion on how best to undertake DA1/1 checks (the same differences of opinion also apply to the “action/resistance factor” Design Approach 2, DA2, checks). This can lead to inconsistent application of Eurocode 7 when undertaking a numerical analysis, which in turn can lead to differences in the resulting design solutions. In this two-part paper, a simple and consistent methodology for undertaking “action/resistance factor” design checks using numerical methods is proposed in Part I, while in Part II the methodology is used to develop a general-purpose design procedure which is then applied to a number of example problems.

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

Direct methods can be used to rapidly verify the safety of solid bodies and structures against collapse, and also to assist engineers wishing to rapidly identify structurally efficient designs for a specified load carrying capacity. Layout optimization is a direct method that can be used to solve very large-scale problems when adaptive solution schemes are employed, and the same underlying mathematical formulation is applicable to both analysis and design problems. Here the truss layout optimization formulation is applied to various benchmark design problems and the discontinuity layout optimization formulation applied to various plane strain limit analysis problems. It is observed that highly accurate solutions can be obtained, close to known analytical solutions. Finally future directions in the field of layout optimization are briefly considered.

Lateral Soil Resistance for On-bottom Pipeline Design on Clayey Seabed

A series of physical model tests were conducted to investigate the lateral resistance of a partially embedded pipe in soft clay under various embedment and loading conditions at both small and large lateral displacements. Computational limit analyses using a technique called Discontinuity Layout Optimisation (DLO) were conducted to back-analyse and compare with the experimental results. It was found that pipes with different over-penetration ratios show different failure modes and pipe trajectories during lateral movements. Based on the numerical and experimental results, a set of design equations are proposed for the predictions of the lateral resistance of a partially embedded pipe under combined vertical and horizontal loads, which can be used by pipeline engineers to predict the post-buckling configuration given the structural properties of the pipeline.

The Ultimate Uplift Capacity of Multi-Plate Anchors in Undrained Clay

Soil anchors are commonly used as foundation systems for structures requiring uplift resistance such as transmission towers, or for structures requiring lateral resistance, such as sheet pile walls. Anchors commonly have more than one plate or bearing element and therefore there is a complex interaction between adjacent plates due to overlapping stress zones. This interaction will affect the failure mode and ultimate capacity. However, no thorough numerical analyses have been performed to determine the ultimate pullout loads of multi—plate anchors. The primary aim of this research paper is to use numerical modeling techniques to better understand plane strain multi-plate anchor foundation behavior in clay soils.

A Thermally Controlled Test Chamber for Centrifuge and Laboratory Experiments

This note describes a novel approach for the provision of a thermally controlled testing chamber. The main principal of the system is to use a layer of cooled air as an active insulation medium to convect away heat transferred through conventional passive insulation. Results from laboratory floor and centrifuge tests are reported. Observed and predicted performance capabilities of the chamber are also discussed.