A new hybrid-Trefftz triangular and quadrilateral plate elements

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We develop 9 DOF triangular and 12 DOF quadrilateral plate bending elements based on the hybrid-Trefftz method. Among the two independent displacement fields, i.e. the internal and the boundary displacements, we use the Mindlin-Reissner's thick plate solution with a particular solution under pressure load as the internal displacement field. For the boundary displacement field, we approximate transverse displacement (w) over tilde and rotations (beta) over tilde (x) and (beta) over tilde (y) cubic and quadratic hierarchical shape functions, respectively. We derive the transverse shear strains from constitutive equations and equilibrium equations, respectively, and then, remove additional degrees of freedom of hierarchical shape functions using the relations between these two shear strains. Results of numerical tests reveal that the new triangular (T32 - 7) and quadrilateral (Q32 - 11) elements are robust, accurate and free of shear locking in the thin limit. (C) 2009 Elsevier Inc. All rights reserved.
Publisher
ELSEVIER SCIENCE INC
Issue Date
2010-01
Language
English
Article Type
Article
Keywords

SHEAR STRAIN FIELDS; FINITE-ELEMENT; INCOMPATIBLE MODES; BENDING ELEMENTS; THICK

Citation

APPLIED MATHEMATICAL MODELLING, v.34, no.1, pp.14 - 23

ISSN
0307-904X
DOI
10.1016/j.apm.2009.03.022
URI
http://hdl.handle.net/10203/99147
Appears in Collection
ME-Journal Papers(저널논문)
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