Three dimensional piezoelectric boundary elements

Lisa R. Hill, Thomas N. Farris

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


The boundary element method is applied to problems of 3D piezoelectricity. The continuum equations for the mechanical and electrical behavior are combined into one governing equation for piezoelectricity. A single boundary integral equation is developed from this combined filed equation and the Green's solution for a piezoelectric medium. The Green's function and its derivatives are derived using the Radon transform, and the resulting solution is represented by a line integral which is evaluated numerically using standard Gaussian quadrature. The boundary integral equation is discretized using 8-node quadrilateral elements resulting in a matrix system of equations. The solution of the boundary problem for piezoelectric materials consists of elastic displacements, tractions, electric potentials and normal charge flux densities. The field solutions can be obtained once all boundary values have been determined. The accuracy of this piezoelectric boundary element method is illustrated with two numerical examples. The first involves a unit cube of material with an applied mechanical load. The second example consists of a spherical hole in an infinite piezoelectric body loaded by a unit traction on its boundary. Comparisons are made to the analytical solution for the cube and axisymmetric finite element results for the spherical hole. The boundary element method is shown to be an accurate solution procedure for general 3D piezoelectric materials problems.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherSociety of Photo-Optical Instrumentation Engineers
Number of pages12
ISBN (Print)0819424528
StatePublished - Dec 1 1997
Externally publishedYes
EventSmart Structures and Materials 1997: Mathematics and Control in Smart Structures - San Diego, CA, USA
Duration: Mar 3 1997Mar 6 1997

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherSmart Structures and Materials 1997: Mathematics and Control in Smart Structures
CitySan Diego, CA, USA

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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    Hill, L. R., & Farris, T. N. (1997). Three dimensional piezoelectric boundary elements. In Proceedings of SPIE - The International Society for Optical Engineering (pp. 406-417). (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 3039). Society of Photo-Optical Instrumentation Engineers.