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hp ‐Clouds in Mindlin's thick plate model
Author(s) -
Garcia Oscar,
Fancello Eduardo A.,
de Barcellos Clovis S.,
Duarte C. Armando
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000320)47:8<1381::aid-nme833>3.0.co;2-9
Subject(s) - galerkin method , mathematics , cloud computing , meshfree methods , stiffness matrix , finite element method , wavelet , kernel (algebra) , degree of a polynomial , discontinuous galerkin method , mathematical analysis , polynomial , computer science , structural engineering , engineering , artificial intelligence , pure mathematics , operating system
In the last few years a number of numerical procedures called as meshless methods have been proposed. Among them, we can mention the diffuse 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 first 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 finite element method, namely, the shear locking can be controlled by using hp cloud approximations of sufficiently high polynomial degree. The computational implementation of the method and the issue of numerical integration of the stiffness matrix are also discussed. Copyright © 2000 John Wiley & Sons, Ltd.