hp-Clouds in Mindlinʹs thick plate model

In the last few years a number of numerical procedures called as meshless methods have been proposed. Among them, we can mention the di use element method, smooth particle hydrodynamics, element free Galerkin method, reproducing kernel particle method, wavelet Galerkin methods, and the so-called hp-cloud method. The main feature of these methods is the construction of a collection 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 knowledge, the rst results concerning the behaviour of this technique on the solution of Mindlinʹs moderately thick plate model. It is demonstrated numerically that the behaviour of the method with respect to shear locking is essentially the same as in the p-version of the nite element method, namely, the shear locking can be controlled by using hp cloud approximations of su ciently high polynomial degree. The computational implementation of the method and the issue of numerical integration of the sti ness matrix are also discussed.