Absolute nodal coordinate formulation of large-deformation piezoelectric laminated plates

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 MUL-TIPHYSICS (http://www.comsol.com/) is carried out with an excellent agreement.

A Continuum Based Three-Dimensional Modeling of Wind Turbine Blades

“…Where c E is the elastic coefficient matrix for homogeneous isotropic material [10]. The membrane and shear strain vector e m is defined as:…”

“…The curvature vector j ¼ j xx j yy 2j xy ½ T can be expressed in terms of the gradient vectors as the following relations [10]:…”

“…The modeling computation problem increases as the rotor blade diameter increases. For instance, the Enercon E-126 is the largest wind turbine model built to date, manufactured by the German wind tur- The recently developed ANCF had been used in the analysis of large deformation of flexible multibody systems including belt drives [6][7][8], rotor blade [9], large deformation piezo-electric laminated plates [10], flexible robotic manipulators [4], and cable applications [11]. The important advantage of using this formulation in multibody computer simulations is the constant mass matrix that can be obtained for fully nonlinear dynamic problems.…”

Analysis of electromechanical systems based on the absolute nodal coordinate formulation

“…ANCF beam elements within the framework of the Euler-Bernoulli beam theory assumption were used to simulate the performance of surface-bonded piezoelectric actuators [10]. Later, [28] successfully extended the ANCF approach to simulate piezoelastic laminated plates. Other attempts to apply the ANCF to MEMS simulations have been reported by [23,38].…”

A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates

“…Recently, deformations of plates composed of various materials and new techniques of computations have been studied. In [28], by using the absolute nodal coordinate formulation, large deformations of piezoelectric laminated plates were analyzed, and the numerical results were compared with the results obtained from COMSOL (see also [29][30][31][32][33][34]). In this context, it is noteworthy to recall also some models of a mixed assumed strain finite element developed for laminated plates as done in [35,36].…”