SUMMARYIn 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 ÿrst results concerning the behaviour of this technique on the solution of Mindlin's 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 ÿnite 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.

This paper develops and analyzes two techniques to extend the use of generalized finite element method techniques to structural shell problems. The first one is a procedure to define local domains for enrichment functions based on the use of pseudo-tangent planes. The second one is a procedure for imposing homogeneous essential boundary conditions and treatment of boundary layer problems by utilizing special functions. The main idea supporting the pseudo-tangent proposition is the separation of the geometric description, with its intrinsical distortions with respect to the physical domain, from the approximation space, which is defined in a locally undistorted domain. The treatment of essential boundary conditions allows an adequate enrichment in the boundary vicinity, preserving the completeness of the polynomials defining the basis functions. A set of numerical cases are tested in order to show the behavior of the proposed strategies, and a number of observations are drawn from the results, as follows. First, the technique of constructing the enrichment functions on a pseudo-tangent plane shows good results, even with strongly curved shell surfaces. With respect to the locking problem, the method behaves in a similar way as the classical hierarchical finite element methods, avoiding locking for appropriate levels of p-refinements. The procedure considered to impose essential boundary conditions in strong form appears to be more accurate than with the penalty or Lagrange multiplier methods. The inclusion of exponential modes for the treatment of boundary layers in shells provided extremely good results, even with integration elements much larger than the shell thickness.