Abstract
This paper considers the problem of interfacing geometric modelling with finite element analysis in the numerical simulation of the casting process. It is shown that geometrical modellers are capable of describing uniquely the shape of the most complex cast object and that finite element meshes may be constructed within the component. However, such a mesh is defined by the geometry of the object and, hence, may not be the ideal for subsequent simulations. This difficulty is overcome by the use of an adaptive mesh created during the finite element analysis on the basis of information provided by the current solution. The fundamental background to adaptive mesh generation is presented together with the details of its implementation. The method is then applied to the calculation of the flow into a mould cavity from which the accuracy and efficiency of the method is demonstrated. It is concluded that the technique is viable for use with computer-aided design tools for the foundry industry.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Aizawa and T. Umeda: CAD/CAE for casting: State of the art in Japan. In: CADCAM in the Foundry/it, Proceedings 52nd Congress, CIATF (1985).
J.T. Berry and R.D. Pehlke: CADCAM and the simulation of solidification. In: CADCAM in the Foundry/it, Proceedings 52nd Congress, CIATF (1985).
G.L. Bird: The Ford 2.5 litre direct injection, naturally aspirated diesel engine. Proc. Inst. Mech. Engrs. 199 (1985) 122–133.
J.C. Cavendish: Local mesh refinement using rectangular blended finite elements. J. Comp. Phys. 19 (1975) 211–228.
G.S. Cole: Transport processes and fluid flow in solidification. In: Liquid Metals and Solidification. American Society for Metals, Cleveland, Ohio (1958) pp. 201–274.
S.C. Flood and J.D. Hunt: A model of a casting. Appl. Sci. Res. 44 (1987) 27–42.
J. Gago, D.W. Kelly, O.C. Zienkiewicz and I. Babuska: A-posteriori error analysis and adaptive processes in the finite element method. Part II — Adaptive mesh refinement. Int. J. Numer. Methods Engng. 19 (1983) 1621–1656.
I. Imafuku and K. Chijiiwa: A mathematical model for shrinkage cavity prediction in steel castings. Trans. Am. Foundrymen's Soc. 91 (1983) 527–540.
D.W. Kelly, J. Gago, O.C. Zienkiewicz and I. Babuska: A-posteriori error analysis and adaptive processes in the finite element method. Part I — Error analysis. Int. J. Numer. Methods Engng. 19 (1983) 1593–1619.
R.W. Lewis, K. Morgan, R. Pietlicki and T.J. Smith: The application of adaptive mesh methods to petroleum reservoir simulation. Rev. de l'Inst. Français Pet. 38 (1983) 751–761.
R.W. Lewis, K. Morgan, E.D.L. Pugh and T.J. Smith: A note on discontinuous numerical solutions of the kinematic wave equation. Int. J. Numer. Methods Engng. 20 (1984) 555–563.
R.W. Lewis, K. Morgan and P.M. Roberts: Determination of thermal stresses in solidification problems. In: J.F.T. Pitman, O.C. Zienkiewicz, R.D. Wood and J.M. Alexander (eds) Numerical Analysis of Forming Processes. Chichester: John Wiley and Sons (1984) pp. 405–431.
R.W. Lewis and P.M. Roberts: Finite element simulation of solidifcation problems. Appl. Sci. Res. 44 (1987) 61–92.
H.J. Morel-Seytoux: Unit mobility ratio displacement calculations for pattern floods in a homogeneous medium. Soc. Petrol. Engrs. J. 6 (1966) 217–227.
K. Morgan, T.J. Smith, R. Pietlicki, E.D.L. Pugh and R.W. Lewis: The simulation of thermal fronts in petroleum reservoirs during enhanced oil recovery operations. In: R.W. Lewis, J.A. Johnson and W.R. Smith (eds) Numerical Methods in Thermal Problems, Volume III. Swansea: Pineridge Press (1983) pp. 1154–1170.
R. Pietlicki, T.J. Smith, R.W. Lewis and K. Morgan: Adaptive computational grids for EOR simulations. University College of Swansea, Institute for Numerical Methods in Engineering, Preprint (1986) 8 pp.
T.J. Smith, A.F.A. Hoadley and D.M. Scott: On the sensitivity of numerical simulations of solidification to the physical properties of the melt and the mould. Appl. Sci. Res. 44 (1987) 93–109.
R.A. Stoehr and W.-S. Hwang: Modelling the flow of molten metal having a free surface during entry into moulds. In: Modelling of Casting and Welding Processes II. New York: AIME (1985) pp. 47–58.
D.P. Sturge: Improvements to parametric bicubic surface pathches. In: J.A. Gregory (ed.) The Mathematics of Surfaces. Oxford: Oxford University Press (1986) pp. 47–58.
P.A. Walsham and W.A. Knight: Further developments of a geometric modelling system for the computer-aided manufacture of dies and moulds. Annals CIRP 32 (1983) 339–344.
C. Wei, J.T. Berry and P.H. Franklin: Riser design using edge functions. In: Modelling of Casting and Welding Processes II. New York: AIME (1983) pp. 237–242.
D.B. Welbourn: Computer-aided engineering (CADCAM/DUCT) in the foundry. In: Development for Future Foundry Prosperity. Alvechurch: BCIRA (1984) pp. 23–1 to 23–19.
D.B. Welbourn: Full three-dimensional CADCAM. Comput. Aided Engng. J. 1 (1984) 54–60.
D.B. Welbourn: Full three-dimensional CADCAM — Part II. Comput. Aided Engng. J. 1 (1984) 189–192.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Smith, T.J., Welbourn, D.B. The integration of geometric modelling with finite element analysis for the computer-aided design of castings. Applied Scientific Research 44, 139–160 (1987). https://doi.org/10.1007/BF00412010
Issue Date:
DOI: https://doi.org/10.1007/BF00412010