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Proceedings Paper

Three dimensional piezoelectric boundary elements
Author(s): Lisa R. Hill; Thomas N. Farris
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Paper Abstract

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.

Paper Details

Date Published: 13 June 1997
PDF: 12 pages
Proc. SPIE 3039, Smart Structures and Materials 1997: Mathematics and Control in Smart Structures, (13 June 1997); doi: 10.1117/12.276559
Show Author Affiliations
Lisa R. Hill, Purdue Univ. (United States)
Thomas N. Farris, Purdue Univ. (United States)

Published in SPIE Proceedings Vol. 3039:
Smart Structures and Materials 1997: Mathematics and Control in Smart Structures
Vasundara V. Varadan; Jagdish Chandra, Editor(s)

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