DNA-微悬臂梁的Rayleigh-Ritz法求解OA

DNA-microcantilevers hold significant potential in biosensing due to their nanomechanical proper-ties,yet the assumption regarding uniform curvature and axial strain of the neutral axis remains unverified.To address this,a functional potential energy model coupling the free energy of liquid crystalline DNA molecular layers with the composite beam deformation,was established.An innovative triangular series modal superposi-tion approach was used to characterize displacement fields,and enable the variational solution via the Rayleigh-Ritz method,and a segmented integration strategy was employed to realize the full-domain free energy compu-tation.Then the nonlinear equations governing Ritz coefficients were solved through the fixed-point iteration to yield microcantilever deformations and DNA strand spacing distributions.The results indicate that,the de-formed curvature exhibits pronounced uniformity,providing theoretical support for the uniformity assumption.Convergence analysis demonstrates that,the triangular series expansion order≥10 and the number of beam segments divided≥2 500 ensure solution accuracy for deflection and stress,effectively validating the correct-ness of the uniformity assumption within the coupled model.