A Remarkable Tensor in Plane Linear Elasticity

[+] Author and Article Information
Q.-C. He

Laboratory of Applied Mechanics, Department of Mechanical Engineering, Swiss Federal Institute of Technology, CH-1015 Lausanne, Switzerland

J. Appl. Mech 64(3), 704-707 (Sep 01, 1997) (4 pages) doi:10.1115/1.2788952 History: Received July 17, 1996; Revised November 15, 1996; Online October 25, 2007


It is shown that any two-dimensional elastic tensor can be orthogonally and uniquely decomposed into a symmetric tensor and an antisymmetric tensor. To within a scalar multiplier, the latter turns out to be equal to the right-angle rotation on the space of two-dimensional second-order symmetric tensors. On the basis of these facts, several useful results are derived for the traction boundary value problem of plane linear elasticity.

Copyright © 1997 by The American Society of Mechanical Engineers
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