| Despite its importance to the mechanical integrity of engineering components, contact effects are frequently treated using oversimplifying assumptions, leading to inaccurate prediction of the contact stress distribution. This is due to the complexity of the governing system of equations and their behaviour under any design perturbation. In addition, shape optimisation of contact problems constitutes an important field in the design and development of many engineering applications. It is however not commonly used in developing contact surfaces. It is with this in mind that we conduct the current investigations.; This thesis is devoted to the development, implementation and application of optimal shape design of frictional contact problems, using variational inequalities. Three aspects of the work are accordingly examined. The first is concerned with the consistent, accurate and efficient modelling of frictional contact problems. In this regard, accurate representation of contact surfaces using cubic splines and a new surface-to-surface contact search algorithm are developed. To avoid the difficulties associated with nondifferentiability of Coulomb's friction terms, two solution techniques are adopted: (i) mathematical programming along with the use of regularisation and (ii) nondifferentiable optimisation techniques.; The second aspect is concerned with the development of new shape optimisation formulations and algorithms for elastic and elasto-plastic media involving frictional contact. This includes the appropriate selection of objective functions and design variables, which are based on the use of rational B-splines, and the development of new sensitivity analyses using the material derivative approach. Three solution techniques are employed to solve the resulting nonsmooth formulations. The first is based on the use of Sequential Quadratic Programming to minimise the regularised objective function. In the second, nonsmooth objective functions are minimised using proximal bundle method, while the third is based on the use of genetic algorithm.; Finally, the newly developed formulations and algorithms are validated and applied to a number of real engineering problems. The numerical predictions are compared to existing commercial finite element codes. The results revealed that the new consistent contact and optimisation formulations are more accurate and reliable than the traditional contact variational and gradient optimisation methods. |
