Original scientific paper

Thin plate quadrilateral element with independent rotational DOF

Željana Nikolić orcid.org/0000-0002-1097-5739 ; University of Split, Faculty of Civil Engineering, Split, CROATIA
Ante Mihanović ; University of Split, Faculty of Civil Engineering, Split, CROATIA

Abstract

This paper presents a quadrilateral thin plate bending element with 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 the 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 ensure a high order of interpolation for the plate displacement. In both cases, finite element possesses twelve global degrees of freedom. The additional unknowns in the rotational shape functions of an arbitrarily quadrilateral element are eliminated on the element level.

Keywords

thin plate, quadrilateral finite element, independent rotational DOF

Hrčak ID:

316188

URI

https://hrcak.srce.hr/316188

Publication date:

22.12.2003.

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