Kriging-based Finite Element Method for Analyses of Reissner-Mindlin Plates

A class of finite element method using kriging shape functions is developed to analyze Reissner-Mindlin plates. The shape functions are constructed using kriging interpolation (KI) over a set of nodes encompassing a number of layers of elements. In addition to the commonly used gaussian correlation function, a quartic spline function is introduced as the correlation function in the KI. The appropriate ranges of the kriging correletion parameters, both for the gaussian and quartic spline correlation functions, are determined based on the lower and upper bounds proposed by Plengkhom and Kanok-Nukulchai. The discretized equations are formulated using the standard displacementbased finite element procedure on the variational form. The problem domain is discretized using triangular elements. A study on a simply supported square plate is carried out to investigate the shearlocking phenomenon. The study shows that the use of high order basis can alleviate shear locking and the locking disappears if bi-cubic basis is used. When there is no shear locking, the results are insensitive to the change of the type of correlation function.