Modified meshless local Petrov-Galerkin formulations for elastodynamics

International Journal for Numerical Methods in Engineering

Volumn 90, Issue 12, 2012, Pages 1508-1828

  Soares, D ^a   Sladek, V ^b   Sladek, J ^b  

^a FEDERAL UNIVERSITY OF JUIZ DE FORA   (Brazil)

^b INSTITUTE OF CONSTRUCTION AND ARCHITECTURE   (Slovakia)

Author keywords

Analytical integration; Derivatives of shape functions; Elastodynamics; Meshless local Petrov Galerkin formulations; Moving least squares approximation; Taylor series expansion

Indexed keywords

ANALYTICAL INTEGRATION; ELASTO-DYNAMICS; MESHLESS LOCAL PETROV-GALERKIN; MOVING LEAST SQUARES APPROXIMATION; SHAPE FUNCTIONS; TAYLOR SERIES EXPANSIONS;

GALERKIN METHODS; LEAST SQUARES APPROXIMATIONS; ORDINARY DIFFERENTIAL EQUATIONS; TAYLOR SERIES; TIME DOMAIN ANALYSIS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 84861571477     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3373     Document Type: Article

References (18)

1. Belytschko T, Lu Y, Gu L. Element free Galerkin methods. International Journal for Numerical Methods in Engineering 1994; 37:229-256.
2. Wen PH, Aliabadi MH. Evaluation of mixed-mode stress intensity factors by the mesh-free Galerkin method: static and dynamic. Journal of Strain Analysis for Engineering Design 2009; 44:273-86.
3. Atluri SN, Shen S. The Meshless Local Petrov-Galerkin (MLPG) Method. Tech. Science Press: Encino, CA, 2002.
4. th World Congress on Computational Mechanics - WCCM8, Int. Center for Numerical Methods in Engn. (CIMNE), Barcelona, 2008. CD -ROM, ISBN 978-84-96736-55-9.
5. th Conference on Computer Methods in Mechanics - CMM 2009, Univ. of Zielona Gora Press, Poland, 2009; 421-422. ISBN 978-83-7481-245-0.
6. Sladek V, Sladek J, Zhang C. Meshless implementations of local integral equations. In In Mesh Reduction Methods, Brebbia CA (eds). WIT Press: Southampton, 2009; 71-82.
7. Sladek V, Sladek J, Zhang C. Local integral equations combined with mesh free implementations and time stepping techniques for diffusion problems. In Advances in Boundray Element Techniques XI, Zhang C, Aliabadi MH, Schanz M (eds). EC Ltd. Publications: Eastleigh, Hampshire, England, 2010; 441-448.
8. Sladek V, Sladek J. Local integral equations implemented by MLS-approximation and analytical integrations. Engineering Analysis with Boundary Elements 2010; 34:904-913.
9. Sladek V, Sladek J, Zhang C. On increasing computational efficiency of local integral equation method combined with meshless implementations. CMES - Computer Modeling in Engineering & Sciences 2010; 63:243-263.
10. Sladek V, Sladek J, Zhang C. Time integration in solution of diffusion problems by local integral equations and moving least squares approximation. In Boundary Elements and Other Mesh Reduction Methods, Brebbia CA, Popov V (eds). WIT Press: Southampton, 2011; 217-228.
11. Wen PH, Aliabadi MH. An improved meshless collocation method for elastostatic and elastodynamic problems. Communications in Numerical Methods in Engineering 2008; 24:635-651.
12. Houbolt JC. A recurrence matrix solution for the dynamic response of elastic aircraft. Journal of the Aeronautical Sciences 1950; 17:540-550.
13. Long SY, Liu KY, Hu DA. A new meshless method based on MLPG for elastic dynamic problems. Engineering Analysis with Boundary Elements 2006; 30:43-48.
14. Soares D, Sladek J, Sladek V. Non-linear dynamic analyses by meshless local Petrov-Galerkin formulations. International Journal for Numerical Methods in Engineering 2010; 81:1687-1699.
15. Soares D, Sladek J, Sladek V. Time-domain analysis of elastodynamic models by meshless local Petrov-Galerkin formulations. In Advances in Boundray Element Techniques X. Sapountzakis EJ, Aliabadi MH (eds). EC Ltd. Publications: Eastleigh, Hampshire, England, 2009; 375-380.
16. Yang ZJ, Deeks AJ. A frequency-domain approach for transient dynamic analysis using scaled boundary finite element method. Computational Mechanics 2007; 40:725-738.
17. Nowacki W. Dynamic of Elastic Systems. John Wiley & Sons: New York, 1963.
18. Newmark NM.A method of computation for structural dynamics. Journal of Engineering Mechanics Division (ASCE) 1959; 85:67-94.