hp-Clouds in Mindlin's thick plate model

In the last few years a number of numerical procedures called as meshless m ethods have been proposed. Among them, we can mention the diffuse element m ethod, smooth particle hydrodynamics, element free Galerkin method, reprodu cing kernel particle method, wavelet Galerkin methods, and the so-called hp -cloud method. The main feature of these methods is the construction of a c ollection of open sets covering the domain which are used as support of the classical Galerkin approximation functions. The hp-cloud method is focused here because of its advantage of considering from the beginning the h and p enrichment of the approximation space. In this work we present, to our kn owledge, the first results concerning the behaviour of this technique on th e solution of Mindlin's moderately thick plate model. It is demonstrated nu merically that the behaviour of the method with respect to shear locking is essentially the same as in the p-version of the finite element method, nam ely, the shear locking can be controlled by using hp cloud approximations o f sufficiently high polynomial degree. The computational implementation of the method and the issue of numerical integration of the stiffness matrix a re also discussed. Copyright (C) 2000 John Wiley & Sons, Ltd.