FINITE ELEMENT ANALYSIS, SIMPLIFIED BY CONFORMAL MAPPING, OF AN AXISYMMETRIC DIELECTRIC CONSTANT PROBE
N. L. Buck, G. P. Groff, Randy Lee Raper · Transactions of the ASAE · 1999
A finite element analysis was conducted to obtain theoretical capacitance values for an axisymmetricdielectric constant sensor applied to layers of lean and fatty tissues. The sensor was under study as a noninvasive tool fordetermining the fat content of beef cattle and carcasses. A conformal mapping performed on a radial cross-section of theprobe greatly simplified the analysis by eliminating field singularities at the edges of the conductors and correcting largedisparities in the sizes of the elements. This coordinate transformation required a modification of the stiffness formulaused in the finite element analysis. Capacitance values with estimated errors under 0.015% were obtained with a mesh ofunder 2,000 nodes. These values were used to identify deficiencies in an equation, developed from experimental data,relating the probe output to tissue thicknesses and dielectric constants. Theoretical capacitance values were neededbecause experimental error was hindering the development of this equation. The information in this article will be of useto other researchers who are performing axially symmetric finite element analyses or who are interested in dielectricconstant measurements on layered materials.