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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 85
PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING
Edited by: B.H.V. Topping
Paper 50

Adaptive Generation of Arbitrary Grids and its Application in Finite Difference Analysis of Three-Dimensional Continua

G.M. Cocchi

D.A.C.S., University of Ancona, Italy

Full Bibliographic Reference for this paper
G.M. Cocchi, "Adaptive Generation of Arbitrary Grids and its Application in Finite Difference Analysis of Three-Dimensional Continua", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 50, 2007. doi:10.4203/ccp.85.50
Keywords: mean criterion, background arbitrary grid, star size quality parameter, a posteriori truncation error, square medium errors, optimum adaptive grid generation.

Summary
In the present work, as an improvement of the previous proposed methods, the author studies an h and/or h-p adaptive refinement strategy for the three-dimensional elastic static analysis of structures by means of the finite difference method (FDM) with arbitrary grids and compares it with other FEM and Meshless Methods [1].

An automatic grid generation on general three-dimensional domains, based on the simplest background grid of points, is developed in this paper, utilizing the 'point selection criterion' of Cocchi [2] for which the order p of the Taylor expansion may be held constant or may be suited to the displacement gradient at each point, according to a 'posteriori error' estimation based on 'truncation error' analysis.

This work points out the influence of 'star size' reduction, the influence of the increase of order p and the influence of the weight proposed in Liszka [3] and in Benito [4].The solution, relevant to the base grid of points, is utilized for improving the 'star' characteristic by means of a quality parameter.

The proposed 'medium relative distance' criterion and 'minimum relative distance' criterion with the 'mean' criterion for adaptive point generation allow a suitable grid redesign.

The numerical experiments show the fast rate of convergence of the numerical results to the exact solution for a small number of adaptive generations and for a small number of discretization points.

References
1
E. Onate, S. Idelsohn, O.C. Zienkiewicz, R.L. Taylor, C. Sacco, "A Stabilized Finite Point Method for Analysis of Fluid Mechanics Problems", Computer Methods in Applied Mech. and Engng., 139, 315-346,1996. doi:10.1016/S0045-7825(96)01088-2
2
G.M. Cocchi, "The finite difference method with arbitrary grids in the elastic-static analysis of three-dimensional continua", Computers & Structures, 75, (2), 187-208 ,2000. doi:10.1016/S0045-7949(99)00087-5
3
T.J. Liszka, C.A.M. Duarte, W.W. Tworzydlo, "hp-Meshless cloud method", Computer Methods in Applied Mech.and Engng., 139, 263-288, 1996. doi:10.1016/S0045-7825(96)01086-9
4
J.J. Benito, F. Ureña, L. Gavete, "Influence of several factors in the generalized finite difference method", Applied Mathematical Modelling, 25, 1039-1053, 2001. doi:10.1016/S0307-904X(01)00029-4

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