engleski

Thin plate quadrilateral element with independent rotational d.o.f.

This paper presents a quadrilateral thin plate bending element with a full compatibility of displacements and rotations at the nodes. A four-node finite element with independent translational and rotational degree of freedom (DOF) at each node is used. The shape functions for the approximation of the displacements and rotations are different and they are both determined from a complete polynomial of the fourth order. After satisfying conditions for value of the functions and their first derivations at the element nodes, the shape functions consist of a fixed part satisfying the homogeneous differential equation and additional modes. The first one ensures high accuracy of the solution for the finite element with parallel opposite sides (rectangular, parallelogram). The additional modes in the shape functions of the rotational angle can be used for improving a solution in an arbitrarily quadrilateral finite element mesh. Described procedures ensures a high order of interpolation for the plate displacement. In the both case finite element possesses twelve global degrees of freedom. The additional unknowns in the rotational shape functions of arbitrarily quadrilateral element eliminate on the element level.

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

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