engleski

Higher-order linked interpolation in thick plate finite elements

In this paper a family of higher-order linked interpolation functions for the Reissner-Mindlin plate elements is derived. Design of this family of interpolation functions is motivated by the corresponding results for the exact field-consistent interpolation in Timoshenko beam elements of constant cross section which are achieved by solving the ordinary differential equation of the problem and expressing it in terms of the nodal values for the displacements and rotations. As the homogeneous part of the Timoshenko beam ordinary differential equation is given in terms of a finite number of polynomial functions, a finite element of appropriate order can fully reproduce the exact solution provided the loading is also described by polynomials. The Mindlin plate theory shares a number of properties with the Timoshenko beam theory, including the interdependence between the out-of-plane displacement and the rotation fields as well as the well-known shear locking anomaly if these fields are interpolated independently and without resorting to selective integration. An answer to this problem may not be generally sought in the above beam methodology, though, since owing to a more complex structure of the partial differential equation of the problem the solution cannot be expressed in terms of a finite number of parameters. Nevertheless, the field-consistent 1D Timoshenko beam interpolation can be generalised to 2D plate elements by analogy and in this paper we present this approach and apply it to higher-order plate elements.

Mindlin plate ; linked interpolation ; shear locking

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