A refined triangular plate bending finite element

Abstract

The derivation of the stiffness matrix for a refined, fully compatible triangular plate bending finite element is presented. The Kirchhoff plate bending theory is assumed. Six parameters or degrees of freedom are introduced at each of the three corner nodes resulting in an 18 degree of freedom element. This refined element is found to give better results for displacements and particularly for internal moments than any plate bending element, regardless of shape, previously reported in the literature.

Subdivision surfaces: a new paradigm for thin-shell finite-element analysis

“…Unfortunately, for general unstructured meshes it is not possible to ensure C 1 continuity in the conventional sense of strict slope continuity across finite elements when the elements are endowed with purely local polynomial shape functions and the nodal degrees of freedom consist of displacements and slopes only [44]. Inclusion of higher-order derivatives among the nodal variables [2,6] leads to wellknown difficulties, e.g., the inability to account for stress and strain discontinuities in shells whose properties vary discontinuously across element boundaries [44], and, owing to the high order of the polynomial interpolation required, the presence of spurious oscillations in the solution.…”

A general theorem on triangular finite $C^{(m)}$-elements

“…Let n be the degree of this triangular C Cm) -element. As the triangulation is chosen quite arbitrarily the polynomials #, S , 0 (T) (see (1)) are also polynomials of degree n. Thus it holds, with respect to (5) and (6), (21) n> 4m + 2p-2k -2/+L Let us set…”

“…Generalizing BelFs device [1], the number of independent parameters can be reduced by imposing on p(x 9 y) the condition that the derivatives 3…”

The Triangular Hermite Finite Element Complementing the Bogner-Fox-Schmit Rectangle

“…Such two-dimensional elements are mostly developed for triangles: the Argyris triangle [1], the Bell reduced triangle [2], the family of Morgan-Scott triangles [3], the Hsieh-Clough-Tocher macrotriangle [4], the reduced Hsieh-Clough-Tocher macrotriangle [5], the family of Douglas-Dupont-Percell-Scott triangles [6], and the Powell-Sabin macrotriangles [7]. The Fraeijs de Veubeke-Sander quadrilateral [8] and its reduced version [9] are also composed of triangles.…”