Subdivision surfaces: A new paradigm for thin-shell finite-element analysis

International Journal for Numerical Methods in Engineering

Volumn 47, Issue 12, 2000, Pages 2039-2072

  Cirak, Fehmi ^a   Ortiz, Michael ^a   Schröder, Peter ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Finite elements; Shells; Subdivision surfaces

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; INTERPOLATION;

KIRCHHOFF-LOVE THEORY; THIN-SHELL FINITE ELEMENT ANALYSIS;

SHELLS (STRUCTURES);

EID: 0034171519     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000430)47:12<2039::AID-NME872>3.0.CO;2-1     Document Type: Article

References (48)

1. Timoshenko S. Theory of Plates and Shells. McGraw-Hill Book Company: New York, 1940.
2. Green AE, Zerna W. Theoretical Elasticity (2 edn). Oxford University Press: England, 1968.
3. Ciarlet PG. The Finite Element Method for Elliptic Problems. North-Holland: Amsterdam, 1978.
4. Zienkiewicz OC, Taylor RL. The Finite Element Method, vol. 2. McGraw-Hill Book Company: Berkshire, 1989.
5. Argyris JH, Scharpf DW. The sheba family of shell elements for the matrix displacement method. Aeronautics Journal of Royal Aeronautical Society 1968; 71:873-883.
6. Bell K. A refined triangular plate bending finite element. International Journal for Numerical Methods in Engineering 1969; 1:101-122.
7. Ashwell DG, Gallagher RH (eds), Finite Elements for Thin Shells and Curved Members. Wiley: London, 1976.
8. Hughes TJR, Liu WK. Nonlinear finite element analysis of shells: Part ii. Two dimensional shells. Computer Methods in Applied Mechanics and Engineering 1981; 27:167-182.
9. Carey GF, Oden JT. Finite Elements - Computational Aspects. Prentice-Hall: Englewood Cliffs, NJ, 1984.
10. Belytschko T, Stolarski H, Liu WK, Carpenter N, Ong JSJ. Stress projection for membrane and shear locking in shell finite-elements. Computer Methods in Applied Mechanics and Engineering 1985; 51:221-258.
11. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
12. Simo JC, Fox DD. On a stress resultant geometrically exact shell model. Part i: formulation and optimal parameterization. Computer Methods in Applied Mechanics and Engineering 1989; 72:267-304.
13. Simo JC, Fox DD, Rifai MS. On a stress resultant geometrically exact shell model. Part ii: the linear theory; computational aspects. Computer Methods in Applied Mechanics and Engineering 1989; 73:53-92.
14. Simo JC, Fox DD, Rifai MS. On a stress resultant geometrically exact shell model. Part iii: computational aspects of the nonlinear theory. Computer Methods in Applied Mechanics and Engineering 1990; 79:21-70.
15. Simo JC, Kennedy JG. On a stress resultant geometrically exact shell model, part v. nonlinear plasticity: formulation and integration algorithms. Computer Methods in Applied Mechanics and Engineering 1992; 96:133-171.
16. Büchter N, Ramm E. Shell theory versus degeneration-a comparison in large rotation finite element analysis. International Journal for Numerical Methods in Engineering 1992; 34:39-59.
17. Andelfinger U, Ramm E. Eas-elements for two dimensional, three dimensional, plate- and shell structures and their equivalence to hr-elements. International Journal for Numerical Methods in Engineering 1993; 36:1311-1337.
18. Roehl D, Ramm E. Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept. International Journal of Solids and Structures 1996; 33:3215-3237.
19. Wriggers P, Eberlein R, Reese S. A comparison of 3-dimensional continuum and shell elements for finite plasticity. International Journal of Solids and Structures 1996; 33:3309-3326.
20. Bucalem ML, Bathe KJ. Finite element analysis of shell structures. Archives of Computer Methods in Engineering 1997; 4:3-61.
21. MacNeal RH. Perspective on finite elements for shell analysis. Finite Element Analysis Design 1998; 30:175-186.
22. Catmull E, Clark J. Recursively generated b-spline surfaces on arbitrary topological meshes. Computer Aided Design 1978; 10(6):350-355.
23. Doo D, Sabin M. Behaviour of recursive division surfaces near extraordinary points. Computer Aided Design 1978; 10(6):356-360.
24. Loop C. Smooth subdivision surfaces based on triangles. Master's Thesis, University of Utah, Department of Mathematics, 1987.
25. Dyn N, Levin D, Gregory JA. A butterfly subdivision scheme for surface interpolation with tension control. ACM Transactions of the Graphics 1990; 9(2):160-169.
26. Reif U. A unified approach to subdivision algorithms near extraordinary vertices. Computer Aided Geometric Design 1995; 12(2):153-174.
27. 1-continuity of subdivision surfaces. SIAM Journal of Numerical Analysis 2000, in print.
28. Stam J. Fast evaluation of loop triangular subdivision surfaces at arbitrary parameter values. In Computer Graphics (SIGGRAPH '98 Proceedings, CD-ROM supplement), 1998.
29. Rojek J, Onate E, Postek E. Application of explicit fe codes to simulation of sheet and bulk metal forming processes. Journal of the Materials Processing Technology 1998; 80:620-627.
30. Kagan P, Fischer A, Bar-Yoseph PZ. New b-spline finite element approach for geometrical design and mechanical analysis. International Journal for Numerical Methods in Engineering 1998; 41:435-458.
31. Kobbelt L, Hesse T, Prautzsch H, Schweizerhof K. Iterative mesh generation for fe-computations on free form surfaces. Engineering Computation 1997; 14:806-820.
32. Naghdi PM. The theory of shells. Handbuch der Physik, Mechanics of Solids II, vol. VI a/2. Springer: Berlin, 1972.
33. Basar Y, Krätzig WB. Mechanik der Flächentragwerke. Friedr. Vieweg & Sohn: Braunschweig, 1985.
34. Strang G, Fix GJ. An Analysis of the Finite Element Method. Prentice-Hall: Englewood Cliffs, NJ, 1973.
35. Schweitzer JE. Analysis and Application of Subdivision Surfaces. Ph. D. Dissertation, Department of Computer Science and Engineering, University of Washington, Seattle, 1996.
36. Zorin D, Schröder P (eds), Subdivision for Modeling and Animation, Computer Graphics (SIGGRAPH '99 Course Notes), 1999.
37. Zorin D, Schröder P, Sweldens W. Interpolating subdivision for meshes with arbitrary topology. In Computer Graphics (SIGGRAPH '96 Proceedings), 1996.
38. Reif U, Schröder P. Curvature smoothness of subdivision surfaces, submitted for publication.
39. Deslauriers G, Dubuc S. Interpolation dyadique. In Fractals, Dimensions Non Entières et Applications. Masson: Paris, 1987; 44-45.
40. Hoppe H, DeRose T, Duchamp T, Halstead M, Jin H, McDonald J, Schweitzer J, Stuetzle W. Piecewise smooth surface reconstruction. In Computer Graphics (SIGGRAPH '94 Proceedings), 1994.
41. Biermann H, Levin D, Zorin D. Smooth subdivision surfaces with normal control. Preprint, Courant Institute of Mathematical Sciences, New York, 1999.
42. Warren J. Subdivision methods for geometric design. Unpublished manuscript, Department of Computer Science, Rice University, November 1995.
43. Kobbelt L, Campagna S, Seidel HP. A general framework for mesh decimation. In Graphics Interface 98, Robins Southern Printing: Vancouver, BC, 1998; 43-50.
44. Lee A, Sweldens W, Schröder P, Cowsar L, Dobkin D. Maps: multiresolution adaptive parameterization of surfaces. In Computer Graphics (SIGGRAPH '98 Proceedings), 1998.
45. Stam J. Fast evaluation of catmull-clark subdivision surfaces at arbitrary parameter values. In Computer Graphics (SIGGRAPH '98 Proceedings), 1998.
46. Haußer C. Effiziente Dreieckselemente für Flächentragwerke. Ph.D. Dissertation, Institut for Structural Mechanics, University Stuttgart, Stuttgart, Germany, 1996.
47. Batoz JL. An explicit formulation for an efficient triangular plate-bending element. International Journal for Numerical Methods in Engineering 1982; 18:1077-1089.
48. Zorin D, Schröder P, Sweldens W. Interactive multiresolution mesh editing. In Computer Graphics (SIGGRAPH '97 Proceedings), 1997.