Anisotropic hierarchic finite elements for the simulation of piezoelectric smart structures

Purpose – Piezoelectric actuators and sensors are an invaluable part of lightweight designs for several reasons. They can either be used in noise cancellation devices as thin‐walled structures are prone to acoustic emissions, or in shape control approaches to suppress unwanted vibrations. Also in Lamb wave based health monitoring systems piezoelectric patches are applied to excite and to receive ultrasonic waves. The purpose of this paper is to develop a higher order finite element with piezoelectric capabilities in order to simulate smart structures efficiently.Design/methodology/approach – In the paper the development of a new fully three‐dimensional piezoelectric hexahedral finite element based on the p‐version of the finite element method (FEM) is presented. Hierarchic Legendre polynomials in combination with an anisotropic ansatz space are utilized to derive an electro‐mechanically coupled element. This results in a reduced numerical effort. The suitability of the proposed element is demonstrated usi...

[1]  Hyun-Jung Kim,et al.  Isogeometric analysis for trimmed CAD surfaces , 2009 .

[2]  Ulrich Gabbert,et al.  Adaptive finite elements methods for virtual engineering design , 2008 .

[3]  K. Y. Sze,et al.  Stabilized plane and axisymmetric piezoelectric finite element models , 2004 .

[4]  Christian Willberg,et al.  Development, Validation and Comparison of Higher Order Finite Element Approaches to Compute the Propagation of Lamb Waves Efficiently , 2012 .

[5]  Ulrich Gabbert,et al.  Numerically Efficient Finite Element Formulation for Modeling Active Composite Laminates , 2006 .

[6]  Jean Lefèvre,et al.  Finite-Elemente-Simulation adaptiver Leichtbaustrukturen zur Untersuchung der Schwingungs- und Schallreduktion , 2006 .

[7]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[8]  T. Hughes,et al.  Finite element method for piezoelectric vibration , 1970 .

[9]  M. G. Milsted,et al.  Use of trigonometric terms in the finite element method with application to vibrating membranes , 1974 .

[10]  Elmar Breitbach,et al.  Adaptive rotor blade concepts: direct twist and camber variation , 2000 .

[11]  Falko Seeger.  Simulation und Optimierung adaptiver Schalenstrukturen , 2003 .

[12]  Adrian Cuc,et al.  Structural Health Monitoring of Adhesively Bonded Joints With Piezoelectric Wafer Active Sensors , 2010 .

[13]  I. Doležel,et al.  Higher-Order Finite Element Methods , 2003 .

[14]  Andrew Y. T. Leung,et al.  FOURIERp-ELEMENT FOR THE ANALYSIS OF BEAMS AND PLATES , 1998 .

[15]  A. Houmat.  AN ALTERNATIVE HIERARCHICAL FINITE ELEMENT FORMULATION APPLIED TO PLATE VIBRATIONS , 1997 .

[16]  Fu-Kuo Chang,et al.  Encyclopedia of structural health monitoring , 2009 .

[17]  Carlos E. S. Cesnik,et al.  Review of guided-wave structural health monitoring , 2007 .

[18]  L. Demkowicz.  One and two dimensional elliptic and Maxwell problems , 2006 .

[19]  H. Lamb.  On waves in an elastic plate , 1917 .

[20]  Victor Giurgiutiu,et al.  7 – PIEZOELECTRIC WAFER ACTIVE SENSORS , 2008 .

[21]  V. Piefort.  FINITE ELEMENT MODELLING OF PIEZOELECTRIC ACTIVE STRUCTURES: SOME AP- PLICATIONS IN VIBROACOUSTICS , 2001 .

[22]  Dragan Marinkovic.  A new finite composite shell element for piezoelectric active structures , 2007 .

[23]  Hazem Kioua,et al.  Piezoelectric induced bending and twisting of laminated composite shallow shells , 2000 .

[24]  Christian Willberg,et al.  Development of a three-dimensional piezoelectric isogeometric finite element for smart structure applications , 2012, Acta Mechanica.

[25]  Ulrich Heisserer,et al.  High-order finite elements for material and geometric nonlinear finite strain problems , 2008 .

[26]  Ernst Rank,et al.  The p‐version of the finite element method for three‐dimensional curved thin walled structures , 2001 .

[27]  Maciej Paszyński,et al.  Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications , 2007 .

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

[29]  Vivar Perez,et al.  Analytical and Spectral Methods for the Simulation of Elastic Waves in Thin Plates , 2012 .

[30]  Christian Becker.  Finite Elemente Methoden zur räumlichen Diskretisierung von Mehrfeldproblemen der Strukturmechanik unter Berücksichtigung diskreter Risse , 2007 .

[31]  Vera Nübel,et al.  Die adaptive rp-Methode für elastoplastische Probleme , 2005 .

[32]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .