hp-Clouds in Mindlin's thick plate model

Abstract

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.

A smoothed finite element method for plate analysis

“…A further extension of the SCNI to analysis of transverse and inplane loading of laminated anisotropic plates with general planar geometry [53] is studied. Other contributions to remove shear locking in meshfree plate discretizations are given in [50,24,32,33,37], and, very recently, [53,19,2].…”

Developments in the application of the generalized finite element method to thick shell problems

“…The enrichment functions L α defined in (4), (6) or (15) are dependent on the local coordinatesx on the pseudo-tangent plane ass seen in (20). Therefore, for a point belonging to an element attached to the vertex X α at elementar intrinsic coordinates (ξ, η), the enrichment functions and their gradients at this point are defined by:…”

A meshfree thin shell method for non‐linear dynamic fracture

“…However, for thin structures, three dimensional modelling of shell structures is computationally expensive. Garcia et al [5] developed meshfree methods for plates and beams; the higher continuity of meshfree shape functions was exploited for Mindlin-Reisner plates in combination with a p-enrichment. Wang and Chen [6] proposed a meshfree method for Mindlin-Reisner plates.…”