Topology Optimization with Geometric Primitives

Structural shapes that can be described by geometric primitives such as bars and plates are commonly encountered in mechanical, aerospace and civil structures. In this thesis, I determine the optimal layout of a set of geometric primitives within a design envelope using topology optimization techniques. To perform the structural and sensitivity analyses of these structures, the geometric primitives are mapped onto a continuous density field defined over a fixed finite element grid via the geometry projection method. As a result, the optimal topology can be more easily fabricated by joining stock structural shapes through various means. Previous works on geometry projection methods only consider minimum compliance for structures made of bars. In this thesis, I formulate topology optimization techniques to design plate structures, and to consider other important structural and manufacturing considerations such as strength, as well as the placement of the primitives to avoid impractical cuts and to ensure a minimum separation between them. I also develop numerical techniques to improve the efficiency and the effectiveness of the proposed methods so that they can be employed in the design of realistic-size problems and to systematically find better local optima.