Meshless local Petrov-Galerkin Euler-Bernoulli beam problems: A radial basis function approach

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

Volumn 4, Issue , 2003, Pages 2475-2488

  Raju, I S ^a   Phillips, D R ^a   Krishnamurthy, T ^a  

^a NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; FUNCTIONS; GALERKIN METHODS; INTERPOLATION; MATRIX ALGEBRA; POLYNOMIALS;

EULER-BERNOULLI BEAM PROBLEM; GENERALIZED MOVING LEAST SQUARES INTERPOLATIONS; MESHLESS LOCAL PETROV-GALERKIN METHOD; RADIAL BASIS FUNCTION;

AEROSPACE ENGINEERING;

EID: 0042512042     PISSN: 02734508     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. Nayroles, B., Touzot, G., and Villon, P. (1992): "Generalizing the finite element method: diffuse approximation and diffuse elements," Computational Mechanics, Vol. 10, pp. 307-318.
2. Belytschko, T., Lu, Y. Y., and Gu, L. (1994): "Element-free Galerkin methods," International Journal for Numerical Methods in Engineering, Vol. 37, pp. 229-256.
3. Atluri, S. N. and Zhu, T. (1998). "A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics," Computational Mechanics, Vol. 22, pp. 117-127.
4. Atluri, S. N., Cho, J. Y., and Kim, H. -G. (1999): "Analysis of thin beams, using the meshless local Petriv-Galerkin method, with generalized moving least squares interpolations," Computational Mechanics, Vol. 24, pp. 334-347.
5. Atluri, S. N. and Shen, S. (2002a): The Meshless Local Petrov-Galerkin (MLPG) Method, Tech Science Press, Encino, CA.
6. Atluri, S. N. and Shen, S. (2002b): "The meshless local Petrov-Galerkin (MLPG) method: a simple & less costly alternative to the finite element and boundary element methods," Computer Modeling in Engineering & Sciences, Vol. 3, No. 1, pp. 11-51.
7. Gu, Y. T. and Liu, G. R. (2001): "A local point interpolating method for static and dynamic analysis of thin beams." Computer Methods in Applied Mechanics and Engineering, Vol. 190, pp. 5515-5528.
8. Krysl, P. and Belytschko, T. (1995): "Analysis of thin plates by the element-free Galerkin method," Computational Mechanics, Vol. 17, pp. 26-35.
9. Donning, B. M. and Liu, W. K. (1998): "Meshless methods for shear-deformable beams and plates," Computer Methods in Applied Mechanics and Engineering, Vol. 152, pp. 47-71.
10. Long, S. and Atluri, S. N. (2002): "A meshless local Petrov-Galerkin method for solving the bending problem of a thin plate," CMES: Computer Modeling in Engineering & Sciences, Vol. 3, No. 1, pp. 53-63.
11. Raju, I. S. and Phillips, D. R. (2002): "A meshless local Petrov-Galerkin method for Euler-Bernoilli beam problems," Proceedings of the ICES '02 Conference, Reno, Nevada, July 31-August 2, 2002, Paper No. 139.
12. Raju, I. S. and Phillips, D. R. (2002): "A local coordinate approach in the MLPG method for beam problems," NASA TM-2002-211463.
13. Phillips, D. R. and Raju, I. S. (2002): "Meshless local Petrov-Galerkin method for bending problems," NASA TM-2002-211936.
14. Raju, I. S. and Phillips, D. R. (2003): "Further developments in the MLPG method for beam problems," CMES: Computer Modeling in Engineering & Sciences, in press.
15. Powell, M.J.D., "The theory of radial basis function approximation in 1990," in Advances in Numerical Analysis, Vol. 2, Clarendon Press, Oxford 1992, pp. 105-210.
16. Wendland, H. (1999): "On the smoothness of positive definite and radial functions," Journal of Computational and Applied Mathematics, pp. 177-188.
17. Wu, Z. (1995): "Compactly supported positive definite radial function," Advances in Computational Mathematics, pp. 283-292.
18. Wang, J. G. and Liu, G. R. (2002): "A point interpolation meshless method based on radial basis functions," International Journal for Numerical Methods in Engineering, Vol. 54, pp. 1623-1648.
19. Wang, J. G. and Liu, G. R. (2002): "On the optimal shape parameters of radial basis functions used for 2-D meshless methods," Computer Methods in Applied Mechanics and Engineering, Vol. 191, pp. 2611-2630.