engleski

Quadrilateral plate element with independent rotational d.o.f.

The finite element models based on the displacement method are very popular in engineering. However, thin plate bending elements based on the Kirchhoff theory may cause unconvergence problems due to C1 continuity requirement. Quadrilateral displacement element with 12 degrees of freedom and a polynomial expression does not satisfy the C1 continuity requirement. Therefore, 12 d.o.f. plate element based on displacement method with the weaker continuity requirement, called non-conforming elements has become a challenge to many researches. Many alternative ways for improving the behaviour of quadrilateral thin plate element in dis-torted mesh have been developed. The most significant of them are: hybrid stress element, discrete Kirchhoff element, generalized conforming element and refined non-conforming element. An alternative way is modelling based on the Reissner-Mindlin theory instead of Kirchhoff the-ory. In this case only C0 shape function continuity is required, hence an interpolation field is more easily constructed. In the most plate elements using Reissner-Mindlin assumptions, the interpola-tion used for the transversal displacements and the rotations involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement, the concept of linked interpolation  1 of the displacement and rota-tions is introduced. An independent representation of translational and rotational field and linking of them can be also used for improving the accuracy and convergence of quadrilateral thin plate element. This paper presents a quadrilateral four-node thin plate bending element with a full compatibil-ity of displacements and rotations at the nodes. The element has independent translational and rota-tional degrees of freedom at each node. This is in accordance with a unified approach to structural system modelling  2 . Similar element with independent translational and rotational d.o.f. and Hermitian shape functions has been developed in  3 . The shape functions for the approximation of the displacement field in this paper are determined from a polynomial of the fourth order. The different interpolation is used for translational and rota-tional part of the displacement field. The chosen shape functions satisfy the homogeneous differen-tial equation of the thin plate bending and ensures a high order of interpolation for the plate dis-placement. The developed quadrilateral element has 12 degrees of freedom and posses very good performances.

thin plate; quadrilateral finite element; independent rotationa d.o.f.

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