Analysis of an elongated stretched strip, with application to a strain-gage electrical sensor design

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2011-04, Vol.91 (4), p.330-338
• Main Authors: Suhir, E., Gschohsmann, W., Nicolics, J.
• Format: Article
• Language: English
• Subjects: actuators; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Elongated elastic strip; Exact sciences and technology; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; sensors
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.201000100

A theory‐of‐elasticity‐based analytical (“mathematical”) stress model has been developed for an elongated strip subjected to tensile displacements distributed over one of its long edges. The model is applied to an advanced ceramic strain‐gage electrical sensor design. We have assumed that the mechanical behavior of the gage configured like a thin plate‐like structural element attached to a thick‐ and‐stiff carrier (substrate) can be evaluated by considering the longitudinal cross‐section of the gage and treating it like an elongated long strip. We have assumed also that since the substrate is much thicker and stiffer than the strip, its displacements determine the interfacial displacements of the strip, but not the other way around. The results based on the developed model indicate that the longitudinal displacements in the strip are distributed linearly over the thickness (“height”) of a long‐and‐thin strip (gage), but fade away exponentially in the through‐thickness direction in the case of a short‐and‐thick strip. We conclude that, for accurate enough measurements, long‐and‐thin, rather than short‐and‐thick, strips (gages) should be employed in the application of interest. The obtained results enable one particularly to determine how thick (“high”) such a strip (gage) should be made for the given material and length. Our solution could be useful also in other areas of applied science and engineering, where strip‐like structural elements subjected to the loading of the type in question are employed. A theory‐of‐elasticity‐based analytical stress model has been developed for an elongated strip subjected to tensile displacements distributed over one of its long edges. The model is applied to an advanced ceramic strain‐gage electrical sensor design. The authors have assumed that the mechanical behavior of the gage configured like a thin plate‐like structural element attached to a thick‐and‐stiff carrier (substrate) can be evaluated by considering the longitudinal crosssection of the gage and treating it like an elongated long strip. They have assumed also that since the substrate is much thicker and stiffer than the strip, its displacements determine the interfacial displacements of the strip, but not the other way around. The results based on the developed model indicate that the longitudinal displacements in the strip are distributed linearly over the thickness (“height”) of a long‐and‐thin strip (gage), but fade away exponentially in the through‐thicknes