Assessment of a layerwise mixed least-squares model for analysis of multilayered piezoelectric composite plates

A layerwise mixed finite element model is developed based on the least-squares formulation for the coupled electromechanical static analysis of multilayered plates with piezoelectric and composite layers. The model assumes a layerwise variable description for displacements, transverse stresses and in-plane strains, along with the electrostatic potential, transverse electric displacement and in-plane electric field components, taken as independent variables. This original choice for the layerwise mixed formulation is intended to ensure the a priori and complete fulfilment of the interlaminar C^0 continuity of both mechanical and electrical variables, which is due to compatibility and equilibrium conditions. Numerical applications are shown for assessment of the model predictive capabilities by comparison with available exact three-dimensional solutions, considering multilayered piezoelectric composite plates of various side-to-thickness ratios, under an applied load or surface potential.

[1]  E. Carrera.  Developments, ideas, and evaluations based upon Reissner’s Mixed Variational Theorem in the modeling of multilayered plates and shells , 2001 .

[2]  Dale A. Hopkins,et al.  Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates , 1997 .

[3]  R. Garcia Lage,et al.  Modelling of piezolaminated plates using layerwise mixed finite elements , 2002 .

[4]  Paul R. Heyliger,et al.  Exact Solutions for Simply Supported Laminated Piezoelectric Plates , 1997 .

[5]  Dimitris A. Saravanos,et al.  Exact free‐vibration analysis of laminated plates with embedded piezoelectric layers , 1995 .

[6]  Erasmo Carrera,et al.  Evaluation of Layerwise Mixed Theories for Laminated Plates Analysis , 1998 .

[7]  J. P. Pontaza,et al.  Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics , 2005 .

[8]  Timothy C. Warburton,et al.  Basis Functions for Triangular and Quadrilateral High-Order Elements , 1999, SIAM J. Sci. Comput..

[9]  Gangbing Song,et al.  Vibration control of civil structures using piezoceramic smart materials: A review , 2006 .

[10]  A. K. Noor,et al.  Assessment of computational models for thermoelectroelastic multilayered plates , 1995 .

[11]  C. M. Mota Soares,et al.  A layerwise mixed least-squares finite element model for static analysis of multilayered composite plates , 2011 .

[12]  Klaus-Jürgen Bathe,et al.  The inf–sup condition and its evaluation for mixed finite element methods , 2001 .

[13]  Aghil Yousefi-Koma,et al.  Applications of Smart Structures to Aircraft for Performance Enhancement , 2003 .

[14]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[15]  Paul R. Heyliger,et al.  Static behavior of laminated elastic/piezoelectric plates , 1994 .

[16]  Ayech Benjeddou,et al.  Advances in piezoelectric finite element modeling of adaptive structural elements: a survey , 2000 .

[17]  Erasmo Carrera,et al.  Mixed piezolectric plate elements with continuos transverse electric displacements , 2007 .

[18]  D. Saravanos,et al.  Mechanics and Computational Models for Laminated Piezoelectric Beams, Plates, and Shells , 1999 .

[19]  D. Saravanos,et al.  Coupled discrete-layer finite elements for laminated piezoelectric platess , 1994 .

[20]  Erasmo Carrera,et al.  Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations , 2002 .

[21]  Erasmo Carrera,et al.  Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices , 2002 .

[22]  C. M. Mota Soares,et al.  Analysis of laminated adaptive plate structures using layerwise finite element models , 2004 .

[23]  E. Carrera.  Theories and finite elements for multilayered, anisotropic, composite plates and shells , 2002 .

[24]  Erasmo Carrera,et al.  Classical and mixed finite elements for static and dynamic analysis of piezoelectric plates , 2007 .

[25]  Erasmo Carrera,et al.  A unified formulation for finite element analysis of piezoelectric adaptive plates , 2006 .

[26]  C. M. Mota Soares,et al.  Layerwise mixed least-squares finite element models for static and free vibration analysis of multilayered composite plates , 2010 .

[27]  Inderjit Chopra,et al.  Review of State of Art of Smart Structures and Integrated Systems , 2002 .

[28]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .