| Compliant mechanisms are joint-free monolithic substitutes for multi-membered rigid-body mechanisms. They offer numerous advantages in their manufacturing and performance. This thesis addresses the topology optimization of compliant mechanisms for flexibility, stiffness, and strength. Three new developments are reported. First, in order to take advantage of the computational efficiency of the optimality criteria method, an optimal property for compliant mechanisms is derived for a generalized multi-criteria flexibility-stiffness formulation. This property states that the ratio of the mutual strain energy density to the strain energy density is uniform through out the continuum excluding portions that are bounded by gage constraints. Using this property, robust topology design software, called PennSyn, is developed. With a graphical user interface, PennSyn enables fully automated design of compliant mechanisms from functional specifications to manufacturable form. Second, in order to obtain compliant and strong designs, local failure criteria are included in the topology optimization. Stress constraints are relaxed using quality functions that eliminate the problems associated with singularities. Solutions obtained with the flexibility-strength formulations are observed to be better than those obtained with flexibility-stiffness formulations. Third, geometric nonlinearity associated with large displacements is accounted for in the function evaluation and sensitivity analysis. Using the nonlinear topology optimization algorithm, prescribed nonlinear force-deflection characteristic and curved output path generation are demonstrated. Numerous examples are included to illustrate, analyze, and interpret the problem formulations and algorithms developed in this thesis, including the convexity issues. |
