Membrane Locking and Reduced Integration for Curved Elements

[+] Author and Article Information
H. Stolarski, T. Belytschko

Department of Civil Engineering, The Technological Institute, Northwestern University, Evanston, Il. 60201

J. Appl. Mech 49(1), 172-176 (Mar 01, 1982) (5 pages) doi:10.1115/1.3161961 History: Received April 01, 1981; Revised August 01, 1981; Online July 21, 2009


The behavior of a curved beam element is studied by comparison to an analytic solution. In the curved beam element, curvature effects are incorporated through a “shallow-shell” type theory. It is shown that when low-order, inplane displacement fields are used for the element, the curvature terms increase the bending stiffness due to contributions from the membrane strains; this is called “membrane locking.” Reduced integration yields a bending stiffness, which is in better agreement with the analytic value, and yet it retains the bending-membrane coupling, which is characteristic of curved elements. The results of the analysis are verified by several numerical examples.

Copyright © 1982 by ASME
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