This dissertation addresses the problem of developing theory, algorithms and computational methodology for optimization of structures in contact. Three particular research problems are studied: (i) developing efficient and reliable optimization algorithms for solving structural optimization problems including contact, (ii) creating more realistic state problems for structures in frictional contact, and (iii) developing computational methodology for shape optimization of structures in frictionless contact. The study is limited to structures that are linearly elastic and undergo small deformations.

The main contribution made with respect to research problem (i) is a smoothing algorithm for the nested formulation of the structural optimization problem including contact. Numerical experiments show that the algorithm can produce better designs than the traditional sequential convex programming algorithms used in structural optimization.

With respect to (ii) the main contribution is the formulation of a state problem, the likely-state problem, for structures in frictional contact that does not use the load history. The new state problem is an alternative to the physically unrealistic static friction model used in previous work. The new state problem is also suited for optimization of structures in frictional contact.

With respect to (iii) the main contribution is a computational methodology for shape optimization of structures in frictionless contact, which provides a basis for developing user-friendly structural optimization software. For evaluation a software implementation has been created. This software is the first to combine modern methods such as an adaptive finite element method, an accurate contact solver, and analytic sensitivity analysis in one system. It is also user-friendly and efficient.