Dynamic flexibility analysis aims to describe the operability (controllability, resiliency) of dynamic process systems subject to uncertainties, thus facilitating the integration of process design and control. However, the intrinsic limitations of controllability indices and the computational intractability of the optimization formulations in the state-of-the-art approaches largely prohibit their applicability to large-scale nonlinear processes. In this work, we propose a new framework for dynamic flexibility analysis, where a Lyapunov function is considered as an artificial design decision, so that the feasibility and cost of process operation can be evaluated based on estimating the effect of the uncertainties on the Lyapunov function value. The proposed approach leads to computationally efficient optimization formulations for the flexibility test, flexibility index and optimal process design problems under nonlinear dynamics. A preliminary case study is performed on a two-reactor system.