This presentation was made at the NAFEMS European Conference on Simulation-Based Optimisation held on the 15th of October in London.

Optimisation has become a key ingredient in many engineering disciplines and has experienced rapid growth in recent years due to innovations in optimisation algorithms and techniques, coupled with developments in computer hardware and software capabilities. The growing popularity of optimisation in engineering applications is driven by ever-increasing competition pressure, where optimised products and processes can offer improved performance and cost-effectiveness which would not be possible using traditional design approaches. However, there are still many hurdles to be overcome before optimisation is used routinely for engineering applications.

The NAFEMS European Conference on Simulation-Based Optimisation brings together practitioners and academics from all relevant disciplines to share their knowledge and experience, and discuss problems and challenges, in order to facilitate further improvements in optimisation techniques.

Resource Abstract

Cables are used in many engineering structures, e.g. cable-stayed bridges, deployable structures, suspended roofs, electric transmission lines, guyed towers, and cable-operated machinery. Study of statics and dynamics of cables has a long and rich history, attracted many scientists and engineers. A cable is generally modelled as a perfectly flexible (or non-compressive) 1D continuum with no flexural, torsional, or shear rigidities. It may have initial sag, undergo tension-stiffening and large deflection with loading, exhibiting highly nonlinear behaviour.



In numerical analysis, cables can be most efficiently modelled by the so-called catenary element based on an exact analytical expression for the elastic catenary under small strains.



Since a cable does not take a unique shape before the application of any load, cable shape finding needs to be performed for each cable before the analysis of the whole structure. This is a significant feature for the analysis of structures involving cables. Optimisation is frequently involved in shape finding and the analysis of the whole structure.



Cable shape finding aims to compute an unstressed length and/or tension (an initial stiffness can thus be computed for the structural analysis) under given loading (e.g. self weight) to satisfy the user-specified conditions, which can be a given undeformed length, tension at one end, given maximum vertical sag, or the achievement of the minimum tension at one end. The first two situations can be conveniently solved by the catenary element together with the Newton-Raphson iteration procedure. The requirement for a maximum sag and especially the unknown minimum tension is more difficult to achieve, requiring the use of some efficient searching algorithms.



Cable tuning is frequently performed on structures like cable-stayed bridges to achieve various design criteria or targets, e.g. displacements or bending moments or reactions at some locations. Tuning of a cable involves adjusting its tension by either shortening or lengthening the catenary. Since the catenary element is based on a small strain assumption and cannot resist compression, the change to the tension of a cable needs to be constrained properly; again, efficient optimisation algorithms are essential to the success of cable tuning.



We will report our recent success and the challenges faced when using various optimisation strategies for cable shape finding and cable tuning; illustrative examples on single cables as well as practical cable-stayed bridges will be included.