THREE NODE CURVED FINITE ELEMENTS

Abstract eng:
Finite element discretization of an arbitrary two-dimensional region with curved boundary segments is considered. The interior is covered with convex polygons of n−sides, vide ref. (1). In thermomechanical problems, the finite element shape functions for the interior elements should be able to reproduce the constant temperature and strain fields exactly in regions with piecewise linear boundary segments, i.e., each such element must pass the patch test. In order to attain higher precision, the curved boundary is not approximated with piecewise linear segments. When the interior is covered with Wachspress polygonal elements, curved elements are merely “glued” only on the boundary of convex n−gons. Such curved elements (since they are restricted only to the boundary) do not enter in any arbitrary patch hence are exempt from the reproduction of linear displacement fields associated with constant strains. All elements should abide by the Chebycheff conditions: Ni (x) ≥ 0, x∈Ω (1) in order to be meaningful in interpolating temperature field. Furthermore, the uniform field should be exactly reproduced: Ni (x) = 1, x ∈ Ω (2) Here we construct interpolants Ni , equations (1) and (2) on Ω.

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