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Support Size (support + size)

Distribution by Scientific Domains
Engineering100%

Selected Abstracts

A note on enrichment functions for modelling crack nucleation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003
J. Bellec
Abstract For particular discretizations and crack configurations, the enhanced approximations of the eXtended finite-element method (X-FEM) cannot accurately represent the discontinuities in the near-tip displacement fields. In this note, we focus on the particular case where the extent of the crack approaches the support size of the nodal shape functions. Under these circumstances, the asymptotic ,branch' functions for each tip may extend beyond the length of the crack, resulting in a non-conforming approximation. We explain the limitations of the standard approximation for arbitrary discontinuities, and propose a set of adjustments to remedy the deficiencies. We also provide numerical results that demonstrate the advantages of the modified approximation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

On the optimum support size in meshfree methods: A variational adaptivity approach with maximum-entropy approximants

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010
Adrian Rosolen
Abstract We present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle. The method is based on a variational approach, and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters, here those defining the support size of each basis function. We consider local maximum-entropy approximation schemes, which exhibit smooth basis functions with respect to both space and the discretization parameters (the node location and the locality parameters). We illustrate by the Poisson, linear and non-linear elasticity problems the effectivity of the method, which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A Hermite reproducing kernel approximation for thin-plate analysis with sub-domain stabilized conforming integration

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2008
Dongdong Wang
Abstract A Hermite reproducing kernel (RK) approximation and a sub-domain stabilized conforming integration (SSCI) are proposed for solving thin-plate problems in which second-order differentiation is involved in the weak form. Although the standard RK approximation can be constructed with an arbitrary order of continuity, the proposed approximation based on both deflection and rotation variables is shown to be more effective in solving plate problems. By imposing the Kirchhoff mode reproducing conditions on deflectional and rotational degrees of freedom simultaneously, it is demonstrated that the minimum normalized support size (coverage) of kernel functions can be significantly reduced. With this proposed approximation, the Galerkin meshfree framework for thin plates is then formulated and the integration constraint for bending exactness is also derived. Subsequently, an SSCI method is developed to achieve the exact pure bending solution as well as to maintain spatial stability. Numerical examples demonstrate that the proposed formulation offers superior convergence rates, accuracy and efficiency, compared with those based on higher-order Gauss quadrature rule. Copyright © 2007 John Wiley & Sons, Ltd. [source]