A finite element formulation for smart piezoelectric composite shells: Mathematical formulation, computational analysis and experimental evaluation

Abstract A formulation of a smart shell finite element for laminated curved structures with piezoelectric layers working under either the d31 or d33 effects has been developed in order to simulate dynamic tests. The electrical domain was modeled using a first order theory for the electrical field and a layer-wise approach. The mechanical domain is modeled using a degenerated shell theory with implicit curvature, considering a first order shear deformation theory and an equivalent single layer approach. The final formulation was implemented within Abaqus™ commercial finite element analysis package using its User Element (UEL) subroutine. First, some results provided by the proposed formulation were compared to numerical analyses shown by the literature. Second, the implemented finite element was evaluated using modal and frequency domain experiments for a cantilever aluminum beam with two piezoelectric transducers working under the d31 effects, and a free-free curved composite plate with four piezoelectric transducers working under the d33 effects. Comparisons between the natural frequencies and the frequency response functions amplitudes obtained from the experiments and the computational analyses were performed in order to discuss the limitations and potentialities of the proposed formulation.

[1]  Julián Bravo-Castillero,et al.  Numerical and analytical analyses for active fiber composite piezoelectric composite materials , 2015 .

[2]  Dirk Vandepitte,et al.  A new damage model for composite laminates , 2012 .

[3]  U. Gabbert,et al.  An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites , 2005 .

[4]  Chen Wanji,et al.  Refined triangular element for laminated elastic–piezoelectric plates☆ , 2007 .

[5]  Dimitris A. Saravanos,et al.  Layerwise mechanics and finite element model for laminated piezoelectric shells , 1996 .

[6]  T. Ikeda.  Fundamentals of piezoelectricity , 1990 .

[7]  Ozden O. Ochoa,et al.  Finite Element Analysis of Composite Laminates , 1992 .

[8]  Levent Malgaca,et al.  Integration of active vibration control methods with finite element models of smart laminated composite structures , 2010 .

[9]  Dragan Damjanovic.  Hysteresis in Piezoelectric and Ferroelectric Materials , 2006 .

[10]  Ulrich Gabbert,et al.  Accurate Modeling of the Electric Field within Piezoelectric Layers for Active Composite Structures , 2007 .

[11]  Abdul Hamid Sheikh,et al.  An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates , 2001 .

[12]  Santosh Kapuria,et al.  Coupled efficient layerwise and smeared third order theories for vibration of smart piezolaminated cylindrical shells , 2012 .

[13]  Erasmo Carrera,et al.  Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis , 2011 .

[14]  R. Kar-Gupta,et al.  Electromechanical response of 1–3 piezoelectric composites: An analytical model , 2007 .

[15]  E. Carrera,et al.  Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells , 2006 .

[16]  Mohamad S. Qatu,et al.  Recent research advances on the dynamic analysis of composite shells: 2000-2009 , 2010 .

[17]  E. Carrera,et al.  Variable Kinematic Shell Elements for the Analysis of Electro-Mechanical Problems , 2015 .

[18]  J. Z. Zhu,et al.  The finite element method , 1977 .

[19]  Erasmo Carrera,et al.  Axiomatic/Asymptotic Technique Applied to Refined Theories for Piezoelectric Plates , 2015 .

[20]  Erasmo Carrera,et al.  A unified formulation to assess theories of multilayered plates for various bending problems , 2005 .

[21]  Dirk Vandepitte,et al.  Failure analysis of low velocity impact on thin composite laminates : Experimental and numerical approaches , 2008 .

[22]  Maria Augusta Neto,et al.  A triangular finite element with drilling degrees of freedom for static and dynamic analysis of smart laminated structures , 2012 .

[23]  Li Lu,et al.  Hybrid‐stabilized solid‐shell model of laminated composite piezoelectric structures under non‐linear distribution of electric potential through thickness , 2003 .

[24]  Erasmo Carrera,et al.  Variable kinematics and advanced variational statements for free vibrations analysis of piezoelectric plates and shells , 2010 .

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

[26]  Michael Rose,et al.  High‐performance four‐node shell element with piezoelectric coupling for the analysis of smart laminated structures , 2007 .

[27]  Paulo de Tarso R. Mendonça,et al.  HSDT-Layerwise analytical solution for rectangular piezoelectric laminated plates , 2010 .

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

[29]  Erasmo Carrera,et al.  Piezoelectric shell theories with "a priori" continuous transverse electro-mechanical variables , 2007 .

[30]  J. Ro,et al.  Finite Element Modeling of MFC/AFC Actuators and Performance of MFC , 2001 .