Compliant mechanisms are devices which utilize elastic deformation to emulate the behavior of conventional rigid mechanisms. Structural optimization techniques represent a relatively new approach for automating topology synthesis of compliant mechanisms. A cantilever beam model is presented in order to examine the solution behavior of various objective functions intended for compliant mechanism optimization. The model reveals that objective functions which attempt to simultaneously maximize the flexibility and stiffness of a compliant mechanism can be formulated such that they are not well-bounded. Topology optimization problems using these types of objective functions may exhibit heightened convergence sensitivity with respect to the lower design variable bound. The cantilever beam model is also used to develop a new objective function based on maximizing the energy throughput of a compliant mechanism pushing against an external spring. The objective function shows a well-bounded solution to the simple beam model and consequently exhibits more robust optimization convergence. A simple numerical example is given which demonstrates the heightened robustness of the formulation.