Application of polygonal finite elements in linear elasticity

International Journal of Computational Methods

Volumn 3, Issue 4, 2006, Pages 503-520

  Tabarraei, A ^a   Sukumar, N ^a  

^a University of California   (United States)

Author keywords

Barycentric coordinates; Laplace interpolant; Meshfree methods; Natural neighbors

Indexed keywords

BARYCENTRIC COORDINATES; LAPLACE INTERPOLANT; MESHFREE METHODS;

ELASTICITY; FINITE ELEMENT METHOD; LAPLACE EQUATION; PARTIAL DIFFERENTIAL EQUATIONS; TWO DIMENSIONAL;

COMPUTATIONAL MECHANICS;

EID: 34447504567     PISSN: 02198762     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021987620600117X     Document Type: Article

References (17)

1. Christ, N. H., Friedberg, R. and Lee, T. D. [1982] "Weights of links and plaquettes in a random lattice," Nuclear Physics B. 210 337-346.
2. Dasgupta, G. [2003] "Interpolants within convex polygons: Wachspress' shape functions," Journal of Aerospace Engineering 16, 1-8.
3. Floater, M. S. [2003] "Mean value coordinates," Computer Aided Geometric Design 20, 19-27.
4. Hughes, T. J. R. [1987] The Finite Element Method, Prentice Hall.
5. Malsch, E. A. and Dasgupta, G. [2004] "Interpolations for temperature distributions: A method for all non-concave polygons," International Journal of Solids and Structures 41, 2165-2188.
6. Meyer, M., Lee, H., Barr, A. H. and Desbrun, M. [2002] "Generalized barycentric coordinates for irregular polygons," Journal of Graphics Tools 7, 13-22.
7. Moran, B. and Shih, C. F. [1987] "Crack tip and associated domain integrals from momentum and energy balance," Engineering Fracture Mechanics 27, 615-642.
8. Sibson, R. [1980] "A vector identity for the Dirichlet tesselation," Mathematical Proceedings of the Cambridge Philosophical Society 87, 151-155.
9. Sukumar, N., Moran, B., Semenov, A. Yu and Belikov, V. V. [2001] "Natural neighbor Galerkin methods," International Journal for Numerical Methods in Engineering 50, 1-27.
10. Sukumar, N. [2004] "Construction of polygonal interpolants: A maximum entropy approach," International Journal for Numerical Methods in Engineering 12, 2159-2181.
11. Sukumar, N., Moran, B. and Belytschko, T. [1998] "The natural element method in solid mechanics," International Journal for Numerical Methods in Engineering 43, 839-887.
12. Sukumar, N. and Tabarraei, A. [2004] "Conforming polygonal finite elements," International Journal for Numerical Methods in Engineering 61, 2045-2066.
13. Tabarraei, A. and Sukumar, N. [2005] "Adaptive computations on conforming quadtree meshes," Finite elements in Analysis and Design 41, 686-702.
14. Tada, H., Paris, P. C. and Irwin, G. R. [2000] The Stress Analysis of Cracks Handbook (ASME Press, New York).
15. Timoshenko, S. P. and Goodier, J. N. [1987] Theory of Elasticity (McGraw-Hill, New York).
16. Wachspress, E. L. [1975] A Rational Finite Element Basis (Academic Press, New York).
17. Yau, J., Wang, S. and Corten, H. [1980] "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity," Journal of Applied Mechanics 47, 335-341.