A numerical scheme for geometrically exact flexoelectric microbeams using the weak form quadrature element method

摘要

In this article, a geometrically exact flexoelectric beam model and its weak form quadrature element formulation are established. The coupling of strain gradient and electric field in flexoelectricity involving size effects is taken into account and the resulting C1 continuity requirements are satisfied. The formulation owns the advantage of high-order approximation to circumvent locking problems after discretization. Several numerical examples originating from benchmark nonlinear beam problems are studied to validate the feasibility of the formulation. Compared to existing flexoelectric beam models, the use of geometrically exact beam theory in the present model makes an innovative contribution to analyzing flexoelectric microbeams undergoing large displacements and rotations. This study is a step forward to better understandings of flexoelectric effects on microbeams under large deflections, while also providing a viable approach to predict their nonlinear behaviors in such conditions.

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