Passive-Element Analog Circuits for Three-Dimensional Elasticity

[+] Author and Article Information
R. L. Barnoski

Measurement Analysis Corporation, Los Angeles, Calif.

C. R. Freberg

Mechanical Engineering Dept., University of Southern California, Los Angeles, Calif.

J. Eng. Ind 88(1), 8-16 (Feb 01, 1966) (9 pages) doi:10.1115/1.3670900 History: Received December 15, 1964; Online December 08, 2011


This paper considers the derivation of passive-element electrical analogs for three-dimensional elasticity in rectangular, cylindrical, and spherical polar coordinates. The analogs represent, in finite-difference format, the elastic behavior of differential volumes of material defined by the partial differential equations of linearized elasticity theory. Basically, the circuits are derived by equating the elastic strain energy to the power dissipation in the analog circuit. The analogs discussed here are force-current, displacement-voltage circuits. As compared to the more widely known operational amplifier or “active” electrical analog, these analogs simulate the appropriate equations of the elastic system by “passive” electrical components; i.e., by some combination of resistors, inductors, capacitors, and transformers. Strictly speaking, the circuits shown in this discussion are for static elasticity problems. However, as referenced in the text, these analogs can be converted readily into dynamics circuits by visual inspection of the static analogs.

Copyright © 1966 by ASME
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