Kriging-based Finite Element Methods for Analyses of Shear Deformable Beams and Plates

Tjong, Wong Foek (2013) Kriging-based Finite Element Methods for Analyses of Shear Deformable Beams and Plates. In: The 6th Civil Engineering Conference in Asian Region and Annual HAKI Conference, 20-08-2013 - 22-08-2013, Jakarta - Indonesia.

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Abstract

An enhancement of the finite element method using Kriging interpolation (K-FEM) has been recently developed. The key advantage of this innovative method is that the polynomial refinement can be performed without adding nodes or changing the element connectivity. This paper presents the development of the K-FEM for analyses of shear deformable beams and plates. The discretized equations are formulated using the standard displacement-based finite element procedure on the variational equations of Timoshenko beam and Reissner-Mindlin plate. The transverse displacement and the rotations of the beam and the plates are independently approximated using Kriging interpolation. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. The cubic or quartic polynomial basis functions are utilized to alleviate the shear locking. A series of numerical tests are performed to examine the developed Kriging-based beam and plate elements. The results demonstrate that for the case in which shear locking is not an issue, the elements perform very well.

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