An Automatic Network Analog Computer for the Solution of the Biharmonic Equation

[+] Author and Article Information
J. W. Hlinka

Heat and Mass Flow Analyzer Laboratory, Columbia University, New York, N. Y.

H. G. Landau

Mechanical Engineering Department; Heat and Mass Flow Analyzer Laboratory, Columbia University

V. Paschkis

Mechanical Engineering; Heat and Mass Flow Analyzer Laboratory, Columbia University

J. Appl. Mech 30(1), 109-114 (Mar 01, 1963) (6 pages) doi:10.1115/1.3630054 History: Received May 16, 1961; Revised June 14, 1962; Online September 16, 2011


It is known that the biharmonic equation in two dimensions can be solved by use of a pair of coupled electric resistance networks. In the present paper, a modification of this method is described, involving the use of a controller device of novel design. The controller automatically performs the iterations necessary for the solution of the problem. The procedure is applied to two problems: (a) The deflection of a square plate under uniform load, and (b) a plane-stress problem. Errors are evaluated by comparison with the solutions of the corresponding finite-difference problems and with an analytic solution. The sources of error are discussed and recommendations made for improving the computer accuracy.

Copyright © 1963 by ASME
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