Geometrical Nonlinearity for a Timoshenko Beam with Flexoelectricity

The Timoshenko beam model is applied to the analysis of the flexoelectric effect for a cantilever beam under large deformations. The geometric nonlinearity with von Karman strains is considered. The nonlinear system of ordinary differential equations (ODE) for beam deflection and rotation are derived. Moreover, this nonlinear system is linearized for each load increment, where it is solved iteratively. For the vanishing flexoelectric coefficient, the governing equations lead to the classical Timoshenko beam model. Furthermore, the influence of the flexoelectricity coefficient and the microstructural length-scale parameter on the beam deflection and the induced electric intensity is investigated.

Automated summary

The Timoshenko beam model is used to analyze the flexoelectric effect in a cantilever beam under large deformations, considering geometric nonlinearity and von Karman strains. Nonlinear system of ODEs for beam deflection and rotation are derived, and linearized for each load increment. The study investigates the influence of flexoelectricity coefficient and microstructural length-scale parameter on beam deflection and induced electric intensity.