Shape optimization using constructive representations

It is of great importance to find the best possible material layout or shape for given design objectives and constraints in a product design process. In the last two decades, substantial research efforts have been devoted to develop efficient and robust methods in the held of shape/topology optimization.;Three types of shape optimization problems are considered in literatures: parametric shape optimization, boundary variation based shape optimization, and topology optimization. Each problem relies on different shape representations and addresses different aspects of the design process. These three shape optimization problems also correspond to the three stages of a product design process (in reverse order): conceptual design stage, preliminary design stage and detailed design stage. To improve the product performance and reduce the life-cycle of the product design process, it is desirable to unify these different design stages so that all design considerations may be incorporated into the design process. Therefore the boundaries among these three difference shape optimization problems should be relaxed as opposed to the current state in order to Facilitate design automation.;In an effort to combine different shape optimization processes, two critical components are required: first is the composition of different shapes, second is the shape sensitivity analysis. As the shape composition can be easily achieved by the so-called constructive representations through Boolean set operations, the shape sensitivity analysis for such constructive representations lacks mathematical formulation and efficient computation techniques.;In this thesis, we propose a new method for shape sensitivity analysis of constructive representations. The proposed method provides a mathematical foundation for shape optimization problems with constructively represented geometries. The proposed shape sensitivity analysis method is successfully applied to the shape design problems that combine free-form shapes and parametric features with topological controls.