Keywords: Kirchhoff plate bending, five-node element, refined non-conforming formulation.

Selection of the suitable element is one of the most important steps in the finite element modeling. Although elements used in finite element analysis have ideal shapes, it is almost impossible to model complex systems with a mesh of ideally shaped elements, i.e., elements vary in size, have unequal side lengths, and may be distorted. Obviously, there must then be a requirement for the domain to be in the form of interconnected finite sized elements of different size and shape. The elements having sufficient numbers of nodes and sides are therefore needed between elements patterns with different densities across the domain. At this point, transition regions and so-called transition elements are created in the domain through the process of mesh refinement.

As seen in the literature, the necessity of this issue was also pointed out by several researchers. In their studies, a new quadrilateral five-node hybrid/mixed element HP5 [1,2], and refined element DRMP [3]. were established according to the Reissner-Mindlin plate theory. The main purpose of this research was, therefore, to develop a refined five-node transition plate bending element with four or five sides, a discrete Kirchoff plate (DKP), based on Kirchhoff plate theory by using a refined non-conforming element formulation method.

In this study, a new five-node discrete Kirchhoff plate bending element with four and five sides, DKP, was developed. The equations obtained for this element were derived by using refined non-conforming element formulation based on the Kirchhoff plate theory. The new element formulations were then coded into FEAP, a commercial program, and a new DKP element was developed for use in the corresponding numerical analysis. The convergence and usage along with four-node quadrilateral (DKQ) were investigated and the results of the tests were compared with that of the DKQ element.

The numerical studies demonstrated that the proposed element passed the patch test and possessed invariability with respect to the position of fifth node. The results obtained from the mesh refinement make a positive effect on the accuracy of the solution.

The results of maximum deflection under the given loading and boundary conditions for the proposed element indicated that the rate of convergence is very close to that of the DKQ. The differences obtained in the percent error are very small and show a more rapid converging character with the increasing number of elements.

In conclusion, the proposed five-node DKP element can be used along with the four-node DKQ element as a transition element where mesh refinement is necessary. Another future use of this formulation and coding is that it can be employed to analyze both DKQ and DKP elements separately.

1

A.F. Saleeb, T.Y. Chang, "On the hybrid-mixed formulation of C0 curved beam elements", Comput. Methods Appl. Mech. Enging., 60, 95-121, 1987. doi:10.1016/0045-7825(87)90131-9

2

Mei Duan, Yutaka Miyamoto, Shoji Iwasaki, Hideaki Deto, "5-node hybrid/mixed finite elements for Reissner-Mindlin plate", Finite Elements Anal. Des. 33, 167-185, 1999. doi:10.1016/S0168-874X(99)00020-7

3

H. Sofuoglu, H. Gedikli, "A Refined 5-node Plate Bending Element Based on Reissner-Mindlin Theory", Communications in Numerical Methods in Engineering, 23, 385-403, 2007. doi:10.1002/cnm.914

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