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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 75
PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar
Paper 22
Representing Traction Free Boundaries using Drilling Degrees of Freedom A.A. Groenwold+, Q.Z. Xiao* and N.J. Theron+
+Department of Mechanical and Aeronautical Engineering, University of Pretoria, South Africa
Full Bibliographic Reference for this paper
A.A. Groenwold, Q.Z. Xiao, N.J. Theron, "Representing Traction Free Boundaries using Drilling Degrees of Freedom", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Sixth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 22, 2002. doi:10.4203/ccp.75.22
Keywords: traction free, finite element, assumed stress, drilling degrees of freedom.
Summary
This paper investigates new methodologies for the accurate representation
of traction free sides using membrane finite elements with drilling degrees
of freedom and an assumed stress interpolation.
Firstly, a method based on direct enforcement of the traction free condition through manipulation of the assumed stress field of an element is presented (e.g. see Xiao et al. [1]). Secondly, a penalty-equilibrated approach, in which stress equilibrium is enforced in individual elements, is presented (e.g. see Wu and Cheung [2]). In the penalty-equilibrated approach, weak enforcement of equilibrium is proposed herein, in which the stress derivatives are modified as to alleviate locking-like behavior.
The methodologies are applied to the families of assumed stress membrane finite
elements with drilling degrees of freedom recently proposed by Geyer and Groenwold
[3], for which the potential energy is given by
This formulation results in three independent interpolation fields arising from the translations, rotations and the stress assumption. Rather conventional, the stress field is constructed as ![]() ![]() ![]() ![]() ![]() ![]() ![]()
Direct enforcement of the traction free condition:
Writing the traction free condition under consideration as
Penalty equilibrated version of the element: Ignoring the effect of distributed loads within elements, element equilibrium is written as
where ![]() ![]() with ![]() ![]() ![]() ![]()
Four elements are formulated, namely HB12 ![]() ![]() ![]() ![]() ![]() ![]()
References
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