It is becoming increasingly more straightforward to carry out computation using numerical simulation to examine many complex structural and fluid mechanics problems. With readily available high-speed computing, and with techniques to parallelise processing, massive assemblies of equations can be solved reasonably quickly. Methods such as finite-element analysis have grown with this technology. However, there remain many simplifying assumptions. For instance, those required to deal with geometric and physical singularities, and scale effects, that are difficult to include explicitly. Examples include dimensions of problems being reduced to avoid large-scale solid problems, phenomena such as cracking being smeared, multi-physics systems being simplified by decoupling phenomena, and simple turbulence models being used in fluid mechanics to represent far more complex flow patterns. Despite simulation often becoming easier to set up, understanding the boundaries, the simplifying assumptions and model limitations is, perhaps, becoming more important as greater reliance is placed on these techniques. Recognising the need for verification and validation at key stages remains vital, and developments to simplify systems and speed up computation still very relevant.
This issue of Engineering and Computational Mechanics includes six full papers. The first four papers involve structural mechanics, the fifth is based on fluid mechanics and the final paper applies a statistical approach to asset management. Topics covered by these papers are the non-linear solution of deformable systems such as cables, the numerical solutions for displacement, strain and stress fields around cracks using continuous interpolation high order finite elements, the numerical computation of the efficiency of mechanical gearing systems, a study of bracing in trusses including the derivation of three-dimensional (3D) stability functions, an adaptive morphodynamic simulation of shallow flows and, finally, a computational approach to tackling management of strategic railway assets.
The first paper by Razdolsky (2010) describes in a generalised way how two-point non-linear boundary problems in deformable systems can be solved by reduction to a series of linear two-point boundary problems. This process, which involves the combination of a linear set of differential equations where the difference between the equilibrium states is very small as load is raised, is set out using the relationships between displacement and force. As a specific illustration, the equilibrium equations of a flexible cable are solved, including a detailed step-by-step commentary of the principal equation assembly, their derivatives with boundary conditions and the solution. This problem, which considers distributed external loading, one fixed and one sliding support, shows how the technique is able to consider a deformable structure where the solutions for initial geometry and final geometry are very dissimilar. Finally, the author describes the development of a computer program and the process of numerical integration and interpolation to solve the same cable problem.
Papanicolopulos and Zervos (2010) describe numerical solution of crack problems in gradient elasticity where, in addition to strain, second-order derivatives of displacement are considered to effect strain energy. A generalised method of discretisation is presented based on the finite element method that deals with gradient elasticity. As higher order terms are required, the derivation of two-dimensional (2D) triangle and quadrilateral elements and 3D hexahedral elements, all with continuous interpolation, are described. One advantage of these element formulations is that strain gradients are readily available at nodes, so that strains at nodes can be calculated directly without any interpolation. Numerical solutions are then presented for fracture mechanics problems: mode I cracking under tension using a plain strain model; mode II cracking under shear traction using a similar model; mode III cracking under out-of-plane shear traction using a 3D solid model with a suitable reduction in degrees of freedom. The authors show that good correlation of results for mode I cracking is obtained against other published data and conclude that continuous interpolation elements are appropriate for solutions of gradient elasticity problems.
Power transmission by gearing has been at the heart of machinery for centuries where rotating parts are required for propulsion, conveying and cutting/grinding. First appearing in agricultural activities, but then in all manner of industrial, manufacturing and transport systems, gears are universal in their application. Gears allow the direction of motion to be altered, shaft speed to be varied and, used in combinations, provide many complex articulations such as the common place differential units in vehicles. Chaari and Haddar (2010) investigate the mechanical efficiency of spur gears by examining rolling and sliding friction losses and teeth locking to determine the time-dependent efficiency of the system. The computation of mechanical efficiency of a gear system is accomplished by looking at losses in the revolute joint where bearings exist between shafts and gears, and in the contoured joint where teeth meet. Functions for rolling and sliding friction to introduce loss coefficients and the equations for the mechanics of spur gear drive are derived. A numerical example is presented which considers constant sliding and variable sliding friction as well as single and two pair meshed teeth. The authors conclude that mechanical efficiency is time varying and depends on mesh position and teeth-pair contact.
Paper four, by Vieira and Requena (2010), looks at 3D truss stability with particular emphasis on the role of lateral bracing. By considering the elastic behaviour of trusses formed from straight deformable bars, the stiffness matrix technique is used to describe their 3D structural response with both elastic and rigid bracing. Critical loading is determined by geometric non-linear analysis and the corresponding stability functions derived. A computer program was developed to carry out these calculations. The authors use single and paired roof trusses as examples where out-of-plane bracing is examined and the results compared with the results of structural analysis carried out using the finite-element package Ansys.
Huang et al. (2010) describe work involving numerical simulation of sediment transport and morphological change in shallow water flows. A 2D model of bed morphodynamics is developed using the hyperbolic non-linear shallow water equations and the bed deformation equation to represent flow hydrodynamics and bed mophodynamics, respectively. Both series of equations are discretised using finite volumes and dynamically adaptive quadtree grids controlled by seeding points to focus the computational domain. Bed evolution tests are carried out starting with a simple sand bar and comparisons made between an approximate analytical solution, the results from a uniform grid simulation and the results obtained from computationally more efficient adaptive grid simulation. Reasonable agreement is shown. Sand dune and sandpit simulations have also been carried out to demonstrate the improved computational performance of the adaptive grid scheme against uniform grids with results illustrated by bed shape contours and 3D views.
The final paper by Stratford et al. (2010) is not concerned with mechanics, but does describe how through computations a statistical scheme has been developed and applied to the problem of managing a large number of diverse railway civil assets for Network Rail, UK. The paper starts by providing some background to the problem, listing the types of many thousands of bridges, earthworks and coastal defences, and describing past policies that have led to varying levels of maintenance. To manage these assets in the future, Network Rail required a model to forecast expenditure which recognised asset diversity, condition, route policy and longer-term uncertainty. The team used sample sites and levels of maintenance and costs estimated by experienced engineers to avoid prohibitively costly detailed calculations for each asset. To then extrapolate the work on the sample population to the whole asset, a Bayesian statistical approach has been used within a computational framework. The derivation of the estimating equations, variables, approaches to dependency and how these are treated through time is described. The type of engineering work on sampling is summarised and the high-level policy tools described which allow overall future expenditure to be examined for different management approaches. Typical results for bridge stock provide a useful illustration. The authors report that the system developed for strategic asset management modelling is being used successfully by Network Rail for a range of policies covering the long-term management of a very large number of civil assets.
Once again, the editorial panel would like to encourage practitioners to submit short articles on their experience of new or unusual applications of mechanics in civil engineering practice. Such articles would be most welcome, as they would help balance the content of the journal while improving its attractiveness to young engineers working on civil-engineering projects.
