| The objective of this work is to formulate and test continuum topology optimization methods to design both sparse mechanical systems with high buckling stability and hinge free path-following compliant mechanisms.; The first part of the thesis is devoted to compose and implement continuum topology optimization formulations capable of detecting buckling instability in the design process of mechanical systems. Toward this end, two formulations taking buckling into consideration are developed, implemented and compared. In the first, the system is modeled as a hyperelastic continuum at finite deformations and is optimized to maximize the minimum critical bucking load. In the second, the structure under a similar loading is modeled as linear elastic, and the critical buckling load is computed with linearized buckling analysis. Both formulations are found to yield credible structural forms with relatively long tension and short compression members. Specific issues related to achieving the latter objectives are also included in this work, such as a node-based design variable formulation, techniques for eliminating devoid regions from the analysis problem, consistent sensitivity analysis, and perimeter control.; In the second part of the thesis, continuum topology optimization methods are developed to design compliant mechanisms. While most existing continuum topology optimization formulations have the tendency to introduce hinges in the resulting mechanisms, a novel approach is presented in this work to design monolithic hinge free compliant mechanisms. In this respect, artificial springs with predetermined stiffness are used as design aids to control the stiffness of the mechanisms and to ensure their continuity. Many hinge free monolithic compliant mechanisms such as gripper, inverter, and crunch have been successfully designed and tested utilizing this approach.; The final part of the thesis is devoted to obtain formulations and methods to design monolithic hinge free path-following compliant mechanisms. In this respect, a design/control methodology is proposed to control the forces at the input ports of the mechanisms models, such that the mechanisms can follow specified trajectories. In addition, a new continuum topology optimization formulation based on a hyperelastic material model is proposed to design mechanisms that can perform rotation. Many mechanisms are realized utilizing these approaches. |
