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Moving Kriging Interpolation‐based Meshfree Method for Dynamic Analysis of Structures
Author(s) -
Bui Tinh Quoc,
Zhang Chuanzeng
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110090
Subject(s) - diffuse element method , interpolation (computer graphics) , kronecker delta , meshfree methods , galerkin method , discretization , finite element method , kriging , mathematics , moving least squares , mathematical analysis , boundary value problem , weak formulation , newmark beta method , boundary element method , mathematical optimization , computer science , boundary knot method , structural engineering , physics , engineering , animation , statistics , computer graphics (images) , quantum mechanics
A novel meshfree model based on the standard element‐free Galerkin method incorporated moving Kriging interpolation (MK) is developed for free and forced vibration analysis of 2D structures. Instead of employing moving least square approximation (MLS), shape functions here are constructed by the MK method. Due to the satisfaction of the Kronecker delta function, the essential boundary conditions are thus imposed directly as the finite element method and no special techniques are required. Elastodynamic equations are transformed into a standard weak formulation and then discretized into a meshfree time‐dependent equation solved by the standard Newmark time integration method. Some numerical examples of stuctural problems in 2D are attempted, and it is found that the method is adequately accurate and stable for dynamic problems. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)