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An investigation of first‐ and second‐order mixed plate‐bending elements
Author(s) -
Akay H. U.
Publication year - 1980
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620150305
Subject(s) - bilinear interpolation , mathematics , bending moment , polygon mesh , quadratic equation , deflection (physics) , parametric statistics , quadrilateral , mathematical analysis , degenerate energy levels , bilinear form , geometry , finite element method , structural engineering , physics , engineering , classical mechanics , statistics , quantum mechanics
Numerical convergence of first‐ and second‐order plate‐bending elements is investigated. Using iso‐parametric formulation, general bilinear and biquadratic quadrilaterals, with the three moment components and the transverse deflection as dependent variables, are obtained. The same elements are also used as degenerate triangles by collapsing one side. A constant bending moment patch test, applied numerically to the elements, indicated poor performance for linear triangles, while the bilinear, quadratic and biquadratic elements behaved well, with exact results in uniform meshes. Further numerical examples showed the same general trend as the patch test. Although bilinear, quadratic and biquadratic elements were always able to yield the correct solutions with mesh refinements, the linear triangles were in general unable to do so.