Non-Linear Non-Classical Modeling of Microparticles Manipulation Based on Finite Element Method

Abstract

A comprehensive model was presented using the finite element method to analyze the dynamics of cylindrical microparticles, considering non-linear and size effects. The governing equations of motion have been derived based on the weak form method. The stiffness and mass matrices, along with the force vectors, have been presented for non-classical non-linear models of both the Euler–Bernoulli and Timoshenko types. The manipulation dynamics of cylindrical gold microparticles was simulated using FEM. In the simulations, four models of Euler–Bernoulli and Timoshenko beams were utilized. A mesh independence study was investigated. In non-linear models, the stiffness matrix takes into account the effects of higher-order strain terms, leading to a decrease in the maximum bending of the microparticle. The examination of the effects of aspect ratio showed that decreasing it reduces the deflection. After investigating the effects of length scale parameter and aspect ratio, a gold microparticle was manipulated by 200 nm using various models, and the final position of the particle was recorded. To validate the results, the deformations of polystyrene microrods were compared with the available data. The results can be used to make accurate estimates for the positioning of cylindrical microparticles, such as nanowires, nanorods and nanotubes.