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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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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	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 doi:10.4203/ccp.85.50 purchase the full-text of this paper 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 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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