Date of Award
Doctor of Philosophy (PhD)
This thesis introduces a comprehensive computational methodology for the topology optimization of contact problems, which is relevant to a broad range of engineering applications. The proposed methodology is capable of handling geometric and material nonlinearities, unilateral and bilateral contact behavior, small and large contact surface sliding, various contact constitutive relations, and the analysis of both two and three dimensional problems. The Level Set Method (LSM) in combination with the eXtended Finite Element Method (XFEM) is used to provide geometry control while maintaining precise definition of the interface. Contact constitutive relations are enforced weakly at the interface using a surface-to-surface integration method. A nonlinear programming scheme is used to solve the optimization problem, and sensitivities are determined using the adjoint method. To demonstrate mechanical model accuracy and explore the defining characteristics of the proposed method, verification and optimization studies were performed on small strain frictionless contact problems in two dimensions, small strain cohesive problems in two and three dimensions, and large strain frictionless contact problems in two dimensions. The proposed method has shown great promise to achieve optimized geometry for a wide variety of contact behavior. Numerical examples demonstrate that in general, optimal geometry for contact problems depends heavily on the interface constitutive behavior. Three dimensional studies reveal design traits that cannot be characterized in two dimensions. Finally, numerical examples with large sliding contact behavior demonstrate that non-intuitive design solutions can be achieved for surfaces which experience contact over a broad range of motion. Mechanical model accuracy and optimization reliability concerns are discussed for a variety of contact behavioral assumptions and stabilization techniques.
Lawry, Matthew W., "A Topology Optimization Method for Structural Designs Reliant on Contact Phenomena" (2016). Aerospace Engineering Sciences Graduate Theses & Dissertations. 186.