Research Papers

A Mechanical Approach to Solve Two-Dimensional Static Electrical and Magnetic Fields: Applications to Contact Between Conductors Under Electrical Load

[+] Author and Article Information
S. Hao1

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208hao0@suhao-acii.com

Q. Wang, L. M. Keer

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208


Corresponding author.

J. Appl. Mech 77(3), 031013 (Feb 23, 2010) (8 pages) doi:10.1115/1.4000037 History: Received April 11, 2008; Revised September 05, 2008; Published February 23, 2010; Online February 23, 2010

A general approach has been developed to obtain analytical solutions to the boundary-value problems for a two-dimensional conductor under static electric and magnetic fields. This approach is based on a “congruity principle” between a solution of Maxwell’s equation and the corresponding linear elastic plane stress solution with constant mean stress or plane strain solution with constant mean in-plane stress. It also leads to a new avenue to construct analytical solutions of antiplane strain boundary-value problems using plane stress/strain solutions, or vice versa, in linear elastic theory. This approach has been applied for such engineering problems as contact between two conducting solid bodies under electrical load.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

The model analyzed: (a) a rigid conductor contacts a semi-infinite elastic conducting substrate under mechanical pressure and electrical load and the corresponding solutions of Maxwell’s equations can be classified as the boundary-value problems described by (b)

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Figure 2

Analytic solution of an infinitely large conductor plate containing a circular hole under a uniform electrical field E∞ at remote: (a) model analyzed, (b) contours of the electrical potential, and (c) contours of the magnetic field

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Figure 3

The normalized electrical potential (a) and magnetic field (b) for the contact problem in Fig. 1

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Figure 4

Electrical field: (a) the two branches of the Riemann’s surface of Eq. 45, where the branch RII corresponds to the boundary value problem in Fig. 1, and (b) Ey according to Eq. 45

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Figure 5

Contours of electrical potentials for the problem of contact between two semi-infinite conductors; on the contact surface |x|≤1, y=0 the electrical potential 36 is applied with a0=1,ai≠0=0, and the value of conductivity σC in upper semi-infinite conductor is one half of that in the lower plate



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