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$$hp$$-clouds in Mindlin’s thick plate model. (English) Zbl 0987.74067
Summary: 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 focus here is on the $$hp$$-cloud method 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, by performing 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. We also discuss the computational implementation of the method and the numerical integration of stiffness matrix.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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