Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

Applied Mathematical Modelling

Volumn 24, Issue 7, 2000, Pages 439-455

  Fallah, N A ^a   Bailey, C ^a   Cross, M ^a   Taylor, G A ^a  

^a UNIVERSITY OF GREENWICH   (United Kingdom)

Author keywords

Finite element; Finite volume; Geometrically nonlinear

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; FORTRAN (PROGRAMMING LANGUAGE); GALERKIN METHODS; GREEN'S FUNCTION; LAGRANGE MULTIPLIERS; MATRIX ALGEBRA; NONLINEAR EQUATIONS; STRESS ANALYSIS;

GEOMETRICALLY NONLINEAR PROBLEMS; SHAPE FUNCTIONS; WEIGHTED RESIDUAL METHOD; WEIGHTING FUNCTIONS;

MATHEMATICAL MODELS;

EID: 0034207919     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(99)00047-5     Document Type: Article

References (30)

1. Oden J.T., Sato T. Finite strains and displacements of elastic membranes by the finite element method. Int. J. Solids Struct. 3:1967;471-488.
2. J.T. Oden, Finite plain strain of incompressible elastic solids by the finite element method, The Aeronautical Quart. (1968) 254-264.
3. Zienkiewicz O.C., Godbole P.N. Flow of plastic and visco-plastic solids with special reference to extrusion and forming processes. Int. J. Numer. Meth. Eng. 8:1974;3-16.
4. Bathe K.J., Bolourchi S. Large displacement analysis of three dimensional beam structures. Int. J. Numer. Meth. Eng. 14:1979;961-986.
5. Kassimali A., Abbasnia R. Large deformation analysis of elastic space frames. J. Struct. Eng. 117(7):1991;2069-2089.
6. Chin C.K., Al-Bermani F.G.A., Kitipornchai S. Non-linear analysis of thin-walled structures using plate elements. Int. J. Numer. Meth. Eng. 37:1994;1697-1711.
7. Patankar S.V. Numerical Heat Transfer and Fluid Flow. 1980;Hemisphere, Washington, DC.
8. Demirdzic I., Muzaferija S. Finite volume method for stress analysis in complex domains. Int. J. Numer. Meth. Eng. 37:1994;3751-3766.
9. Wheel M.A. A geometrically versatile finite volume formulation for plane elastostatic stress analysis. J. Strain Anal. 31(2):1996.
10. Bailey C., Cross M. A finite volume procedure to solve elastic solid mechanics problems in three dimensions on an unstructured mesh. Int. J. Numer. Meth. Eng. 38:1995;1757-1776.
11. Onate E., Cervera M., Zienkiewicz O.C. A finite volume format for structural mechanics. Int. J. Numer. Meth. Eng. 37:1994;181-201.
12. Wheel M.A. A finite volume method for analysing the bending deformation of thick and thin plates. Comput. Meth. Appl. Mech. Eng. 147:1997;199-208.
13. M.A. Wheel, Applying the finite volume approach to structural analysis, in: S.N. Atluri, P.E. O'Donoghue (Eds.), Modelling and Simulation Based Eng. 1 (1998) 229-234.
14. A. Ivankovic, Finite volume analysis of dynamic fracture problems, in: S.N. Atluri, P.E. O'Donoghue (Eds.), Modelling and Simulation Based Eng. 1 (1998) 180-187.
15. Demirdzic I., Martinovic D. Finite volume method for thermo-elasto-plastic stress analysis. Comput. Meth. Appl. Mech. Eng. 109:1993;331-349.
16. Taylor G.A., Bailey C., Cross M. Solution of the elastic/visco-plastic constitutive equations a finite volume approach. Appl. Math. Modelling. 19:1995;743-760.
17. K. Maneeratana, A. Ivankovic, Finite volume method for geometrically non-linear stress analysis application, Proc. ACME'99, The Seventh Annual Conference of the Association for Computational Mechanics in Engineering, Durham, UK, 1999, pp. 117-120.
18. P. Wenke, M.A. Wheel, Large deformation finite volume method for hyperplastic materials, Proc. ACME'99, The Seventh Annual Conference of the Association for Computational Mechanics in Engineering, Durham, UK, 1999, pp. 113-116.
19. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, Fourth ed., vol. 2, McGraw-Hill, UK, 1991.
20. Malvern L.E. Introduction to the Mechanics of a Continuous Medium. 1969;Prentice-Hall, New york.
21. C. Hirsch, Numerical Computation of Internal and External Flow, vol. 1, Wiley, New York, 1989.
22. Selim V. A node centred finite volume approach: bridge between finite differences and finite elements. Comput. Methods Appl. Mech. Eng. 102:1993;107-138.
23. Finlayson B.A. The Method of Weighted Residuals and Variational Principles. 1972;Academic press, New York.
24. S.S. Rao, in: Robert Maxwell (Ed.), The Finite Element Method in Engineering, 1982.
25. M.A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, vol. 1, Wiley, UK, 1994.
26. Wood R.D., Zienkiewicz O.C. Geometrically nonlinear finite element analysis of beams frames arches and axisymmetric shells. Int. J. Numer. Meth. Eng. 7:1977;725-735.
27. E. Kreyszig, Advanced Engineering Mathematics, Fifth ed., Wiley, New York, 1983.
28. Timoshenko S., Goodier J.N. Theory of Elasticity. 1982;McGraw-Hill, New York.
29. G. Adotte, Second order theory in orthotropic plates, Proceedings, Journal of the Structural Division, ASCE, 93 (ST5, Proc. Paper 5520), October 1967.
30. Bathe K.J. Finite Element Procedures. 1996;Prentice-Hall, New York.