SHAPE OPTIMIZATION IN FRICTIONLESS CONTACT PROBLEMS

A finite element approach for shape optimization in two-dimensional (2-D) frictionless contact problems is presented in this work. The goal is to find the shape that gives a constant distribution of stresses along the contact boundary. The whole formulation, including mathematical model for the unilateral problem, sensitivity analysis and geometry definition is treated in a continuous form, independently of the discretization in finite elements. Shape optimization is performed by direct modification of geometry through B-spline curves an automatic mesh generator is used at each new configuration to provide the finite element input data for numerical analysis and sensitivity computations. Using augmented-Lagrangian techniques (to solve the contact problem) and an interior-point mathematical-programming algorithm (for shape optimization), we obtain several results reported at the end of the article.