Open Access

ARTICLE

A simple locking-free discrete shear triangular plate element

by Y.C. Cai¹, L.G. Tian¹, S.N. Atluri³

1 Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, P.R.China
2 Corresponding author. Email: yc_cai@163.net.
3 Center for Aerospace Research & Education, University of California, Irvine

Computer Modeling in Engineering & Sciences 2011, 77(3&4), 221-238. https://doi.org/10.3970/cmes.2011.077.221

Abstract

A new three node triangular plate element, labeled here as DST-S6 (Discrete Shear Triangular element with 6 extra Shear degrees of freedom), is proposed for the analyses of plate/shell structures comprising of thin or thick members. The formulation is based on the DKT (Discrete Kirchhoff Technique) and an appropriate use of the independent shear DOF(Degrees Of Freedom). The shear locking is completely eliminated in the DST-S6, without any numerical expediencies such as the reduce integration, the use of assumed strains/stresses, or the need for the stabilization of the attendant zero energy modes. It is shown that the present DST-S6 is much simpler than the triangular shear-deformable plate elements currently available which pass the patch test for thick to very thin plates. The DST-S6 has two extra shear DOF per node, but the extra shear DOF are the rotations caused by the transverse shear deformation, and there is no difficulty in applying the essential boundary conditions for the present DST-S6. It is also demonstrated that the solution of a pressure-loaded simply-supported circular plate of the DST-S6 avoids the so-called polygon-circle Paradox. Various numerical examples indicate that the DST-S6 is a robust and high-performance element for thick and thin plates.

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