Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates |
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Authors: | Ayman A Nada Ahmed M El-Assal |
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Institution: | 1.Mechanical Engineering Dept., Benha Institute of Technology,Benha University, Benha, Z.C.,Benha,Egypt |
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Abstract: | The Absolute Nodal Coordinate Formulation (ANCF) has been initiated in 1996 by Shabana (Computational Continuum Mechanics,
3rd edn., Cambridge: Cambridge University Press, 2008). It introduces large displacements of planar and spatial finite elements relative to the global reference frame without
using any local frame. A sub-family of beam, plate and cable finite elements with large deformations are proposed and employed
the 3D theory of continuum mechanics. In the ANCF, the nodal coordinates consist of absolute position coordinates and gradients
that can be used to define a unique rotation and deformation fields within the element. In contrast to other large deformation
formulations, the equations of motion contain constant mass matrices as well as zero centrifugal and Coriolis inertia forces.
The only nonlinear term is a vector of elastic forces. This investigation concerns a way to generate new finite element in
the ANCF for laminated composite plates. This formulation utilizes the assumption that the bonds between the laminae are thin
and shear is non-deformable. Consequently, the Equivalent Single Layer, ESL model, is implemented. In the ESL models, the
laminate is assumed to deform as a single layer, assuming a smooth variation of the displacement field across the thickness.
In this paper, the coupled electromechanical effect of Piezoelectric Laminated Plate is imposed within the ANCF thin plate
element, in such a way as to achieve the continuity of the gradients at the nodal points, and obtain a formulation that automatically
satisfies the principle of work and energy. Convergence and accuracy of the finite-element ANCF Piezoelectric Laminated Plate
is demonstrated in geometrically nonlinear static and dynamic test problems, as well as in linear analysis of natural frequencies.
The computer implementation and several numerical examples are presented in order to demonstrate the use of the formulation
developed in this paper. A comparison with the commercial finite element package COMSOL MULTIPHYSICS () is carried out with an excellent agreement. |
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