AN EFFICIENT LOCKING-FREE COROTATIONAL BEAM 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.