Efficient and accurate deformation analysis of compliant DNA mechanisms based on Timoshenko beam theory

The design and construction of compliant DNA mechanisms have become feasible due to the advances in DNA nanotechnology. However, quantifying their deformation and energy storage capabilities at the nanoscale remains a significant challenge. Accurate and efficient analysis of the mechanical behavior of such mechanisms is essential to enable their precise design and functional regulation. In this work, we leverage the strengths of the Timoshenko Beam Constraint Model (TBCM) to develop DNA-TBCM (DTBCM), a model tailored to describe the deformation behaviors of compliant DNA mechanisms. We investigate the effects of honeycomb and square lattices in compliant DNA links, as well as the influence of nonrigid-fixed junctions and nonuniform cross-sections. Compared with experimental results, our model successfully captures the deformations of compliant DNA hinges and a bistable four-bar linkage. The DTBCM thus provides an efficient and reliable theoretical tool for the structural design and performance optimization of compliant DNA mechanisms, with broad applicability in fields such as atomic manipulation, molecular force sensing, and nanoscale surgery.