Plate Bending Macroelements

  • Christopher G. Provatidis
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 256)


This chapter deals with plate bending analysis applying several CAD-based interpolations. First the performance of boundary-only Coons interpolation is studied; it will be shown that its simplest form coincides with the well-known BFS element of mid-1960s. Then Gordon interpolation is used (i.e., internal nodes are inserted) in order to improve the accuracy of the numerical solution; it will be shown that the Hermite tensor-product element is a special case. The applicability of Bernstein–Bézier interpolation, as a substitute of Lagrange and Hermite polynomials, is discussed in detail. Also, the use of B-splines is examined and it is clearly shown that the barriers are broken when a control points-based tensor product is applied to curvilinear domains. Numerical examples include rectangular and circular thin plates which are solved using a single macroelement.


Plate bending Blending functions C1-continuity Coons formula BFS element Transfinite Tensor-product Hermites Eigenvalues Bernstein–Bézier Beam bending B-splines Rational macroelement Test cases 


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Authors and Affiliations

  1. 1.School of Mechanical EngineeringNational Technical University of AthensAthensGreece

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