Adaptation of the Natural Element method for crack growth simulations

ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering

Volumn , Issue , 2004, Pages

  Ungert, Jörg F ^a   Mostt, Thomas ^a   Bucher, Christian ^a   Könket, Carsten ^a  

^a BAUHAUS UNIVERSITY WEIMAR   (Germany)

Author keywords

Adaptive integration; Crack growth; Meshless; Natural Element Method

Indexed keywords

ADAPTIVE INTEGRATION; COLLABORATIVE RESEARCH; CRACK GROWTH SIMULATION; DISCRETE CRACKS; MESH-LESS METHODS; MESHLESS; NATURAL ELEMENT METHOD; NUMERICAL INTEGRATIONS;

COMPUTATIONAL METHODS; CRACK PROPAGATION; RESEARCH;

CRACKS;

EID: 84893445692     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (19)

1. N. Sukumar, B. Moran, and T. Belytschko. The Natural Element Method in solid mechanics. International Journal of Numerical Methods in Engineering, 43:839-887, 1998.
2. J.R. Shewchuk. Triangle: A two-dimensional quality mesh generator and delaunay triangulator. Technical report, School of Computer Science, Carnegie Mellon University, 1996. download: http://www.cs.cmu.edu/quake/triangle.html.
3. S. Fortune. Computing in Euclidean Geometry, Volume 1 of Lecture Notes Series on Computing, pages 193-233. Du, D.-Z. and Hwang, F.K., 1995.
4. R. Sibson. A vector identity for the dirichlet tesselation. In Mathematical Proceedings of the Cambridge Philosophical Society 87, pages 151-155, 1980.
5. G. Farin. Triangular bernstein-bézier patches. Computer Aided Geometric Design, 3:83-127, 1986.
6. Natarajan Sukumar. Natural Element Method in Solid Mechanics. PhD thesis, Nortwestern university, Illinois, 1998.
7. E. Cueto, M. Doblare, and L. Gracia. Imposing essential boundary conditions in the natural element method by means of density-scaled alpha-shapes. International Journal for for Numerical Methods in Engineering, 49:519-546, 2000.
8. Klaus-Jürgen Bathe. Finite Element Procedures. Prentice Hall, Englewood Cliffs, 1996.
9. D.A. Dunavant. High degree efficient symmetrical gaussian quadrature rules for the triangle. International Journal for for Numerical Methods in Engineering, 21:1129-1148, 1985.
10. S.P. Timoshenko and J.N. Goodier. Theory of Elasticity (Third ed.). McGraw Hill, New York, 1970.
11. M. Brehm and T. Most. A four-node plane EAS-element for stochastic nonlinear materials. In Proceedings of the 16th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering 2003, Weimar, June 2003.
12. D. Gonzáles, E. Cueto, M.A. Martínez, and M. Doblaré. Numerical integration in natural neighbour galerkin methods. International Journal for Numerical Methods in Engineering, submitted 2002.
13. S. De and K.J. Bathe. Towards an efficient meshless computational technique: the method of finite spheres. Engineering Computations, 18:170-192, 2001.
14. J.-S. Chen, C.-T. Wu, S. Yoon, and Y. You. A stabilized conforming nodal integration for galerkin mesh-free methods. International Journal for for Numerical Methods in Engineering, 50:435-466, 2001.
15. L.P. Chew. Guaranteed quality triangular meshes. Technical report, Department of Computer Science, Cornell University, 1989.
16. J. Ruppert. A delaunay refinement algorithm for quality 2-dimensional mesh generation. Journal of Algorithms, 18:548-585, 1995.
17. J.R. Shewchuk. Delaunay Refinement Mesh Generation. PhD thesis, School of Computer Science Pittsburgh, USA, may 1997.
18. L.R. Herrmann. Laplacian-isoparametric grid generation scheme. J. Eng. Mech. Division, ASCE, 102:749-756, 1976.
19. Thomas Most, Christian Bucher, and Jörg F. Unger. Stochastic modeling of cohesive crack propagation using meshless discretization techniques. In P. Neittaanmäki, T. Rossi, K. Majava, and O. Pironneau, editors, Proc. 4th European Congress on Comp. Mechanics in Appl. Sciences and Eng., Jyväskylä, Finland, July 24-28. 2004.