# AN EFFICIENT LOCKING-FREE COROTATIONAL BEAM FINITE ELEMENT

## Palavras-chave:

Piezoelectric beam, Corotational model, Finite element## Resumo

An efficient and accurate locking-free corotational beam finite element is developed in this

work. The element is locally linear, with the displacement varying according to the Timoshenko

assumption and the difference of electric potential varying linearly through each piezoelectric layer

thickness. The shape functions are appropriately derived from the exact solution of the homogeneous

form of the linear equilibrium equations written in terms of displacements, rotations and differences of

electric potential. Since the resulting 2-node element has the same degrees of freedom as the

associated purely mechanical beam element (two displacements and one rotation per node), it can be

directly plugged into an element-independent corotational algorithm to suitably analyze piezoelectric

plane frames under small strains but large rotations. A consistent incremental-iterative technique based

on the Newton-Raphson method is employed for the solution of the nonlinear equilibrium equations.

Numerical examples that demonstrate the efficiency and large rotation capability of the corotational

formulation are presented. The element results are validated by exact solutions available in the

literature. Very good agreement is found in all cases.