Optimizing elastic potential energy via geometric nonlinear stiffness

In this paper, it is shown how a nonlinear elastic mechanical system can be exploited to increase the elastic potential energy compared to its linear counterpart. A strategy for optimizing the system parameters is proposed, and performance is compared considering equal maximum displacement and maximum force. A theoretical insight is presented, and some asymptotic trends for optimum parameters selection are derived in closed-form and highlighted to help the design. A specific nonlinear mechanical system is considered, but the overall approach can be generalized. The actual system consists of a set of linear springs arranged to achieve geometric nonlinearity, and its configuration is selected based on a practical realization. A prototype device is finally assembled and tested to show evidence of the theoretical discussion.