DOI QR코드

DOI QR Code

Finite Element Analysis of Shape Rolling Process using Destributive Parallel Algorithms on Cray T3E

병렬 컴퓨터를 이용한 형상 압연공정 유한요소 해석의 분산병렬처리에 관한 연구

  • Gwon, Gi-Chan (Korea Advanced Institute of Science and Technology) ;
  • Yun, Seong-Gi (Korea Advanced Institute of Science and Technology)
  • Published : 2000.05.01

Abstract

Parallel Approaches using Cray T3E which is NIPP (Massively Parallel Processors) machine are presented for the efficient computation of the finite element analysis of 3-D shape rolling processes. D omain decomposition method coupled with parallel linear equation solver is used. Domain decomposition is applied for obtaining element tangent stifffiess matrices and residual vectors. Direct and iterative parallel algorithms are used for solving the linear equations. Direct algorithm is_parallel version of direct banded matrix solver. For iterative algorithms, the well-known preconditioned conjugate gradient solver with Jacobi preconditioner is also employed. Moreover a new effective iterative scheme with block inverse matrix preconditioner, which is named by present authors, is presented and its results are compared with the one using Jacobi preconditioner. PVM and MPI are used for message passing and synchronization between processors. The performance and efficiency of each algorithm is discussed and comparisons are made among different algorithms.

Keywords

References

  1. Chitkara F. R. and Hardy G. M., 1977, 'Rolling of l-Section Beams Using Lead as a Model Material: Some Experimental Results,' Int. J. Mech. Sci., pp. 575-594 https://doi.org/10.1016/0020-7403(77)90079-0
  2. Altan T., Oh S. I. and Gegel H., 1983, 'Metal Forming Fundamentals and Applications,' American Society of Metals, Metals Park
  3. Altan T. and Fiorentino R. J., 1971, 'Prediction of Loads and Stresses in Closed-Die Forging,' Trans. ASME., pp. 477-484
  4. Oh S. I., 1982, 'Finite Element Analysis of Metal Forming Processes with Arbitrary Shape Dies,' Int. J. Mech. Sci., Vol. 24, pp. 479-493 https://doi.org/10.1016/0020-7403(82)90058-3
  5. Kiuchi M. and Yanagimoto J., 1988, 'Computer Aided Simulation of Shape Rolling Processes,' Proc. of 16th NAMRC, pp. 34-40
  6. Komori K. and Kato K., 1989, 'Analysis of Temperature Distribution in Caliber Rolling of a Bar,' JSME International Jounal, Series. 1, Vol. 32, No. 2, pp. 208-216
  7. Mori K. and Osakada K., 1989, 'Finite Element Simulation of the Three-Dimensional Deformation in Shape Rolling,' Numiform 89, Balkhema Press, Rotterdam, pp. 337-342
  8. Park J.J. and Oh S. I., 1990, 'Application of Three Dimesional Finite Element Analysis to Shape Rolling Processes,' Trans. ASME., Vol.112, pp. 36-46
  9. Mori K., 1990, 'General Purpose FEM Simulator for 3-D Rolling,' Advanced Technology of Plasticity, Vol. 2, pp .619-624
  10. Shin H. W., Kim D. W. and Kim N. S., 1991, 'Finite Element Analysis of I-Section Beam Rolling,' Seoul National University J. Engineering Research, Vol. 23, No. 2
  11. Chen B. K., Thomson P. F. and Choi S. K., 1992, 'Temperature Distribution in the Roll-Gap During Hot Flat Rolling,' J. Mater. Proc. Tech., Vol. 30, pp. 115-130 https://doi.org/10.1016/0924-0136(92)90042-Q
  12. Shin H. W., Kim N. S. and Park J.J., 1993, 'The Analysis of H-Shape Rolling by the Finite Element Method,' J. KSME., Vol. 17, No. 5, pp. 1095-1105
  13. Shin H. W., Kim D. W. and Kim N. S., 1994, 'A Study on the Rolling of I-Section Beams,' Int. J. Mech. Tools Manufact., Vol. 34, No. 2, pp. 147-160 https://doi.org/10.1016/0890-6955(94)90097-3
  14. Badea L. and Gilormini P., 1994, 'Application of a Domain Decomposition Method to Elastoplastic Problem,' Int. J. Solids Structures, Vol. 31, No. 5, pp. 643-656 https://doi.org/10.1016/0020-7683(94)90143-0
  15. Hu N., 1994, 'A Parallel Algorithm for Analyzing Elasto-plastic Problems,' Comput. Struct., Vol. 52, pp. 1127-1133 https://doi.org/10.1016/0045-7949(94)90179-1
  16. Kacou S. and Parsons I.D., 1993, 'A Parallel Multigrid Method for History-dependent Elastoplasticity Computations,' Comput. Methods Appl. Mech. Engrg., Vol. 108, pp. 1-21 https://doi.org/10.1016/0045-7825(93)90150-V
  17. Ferian A., Franchi A. and Genna F., 1996, 'An Incremental Elastic-plastic Finite Element Solver in a Workstation Cluster Environment Part II. Performance of a first Implementation,' Comput. Methods Appl. Mech. Engrg., Vol. 130, pp. 299-318 https://doi.org/10.1016/0045-7825(95)00925-6
  18. Giest A., Begulin A., et al., 1994, Parallel Virtual Machine, A User's Guide and Tutorial for Networked Parallel Computing, MIT Press
  19. Message Interface Forum, 1995, MPI : A Message-Passing Interface Standard, University of Tennessee
  20. GDB/RBD, 1996, MPI Primer/Developing with LAM, Ohio State University
  21. Horie T. and Kuramae H., 1994, 'Evaluation of Parallel Performace of Large Scale Computing using Workstaion Network,' WCCM III, Vol. II, pp. 1569-1570
  22. Shivakumar K.N., Bigelow C.A. and Newman J.C., 1992, 'Parallel Computation in a Three-Dimensional Elastic-Plastic Finite-Element Analysis,' Computers & Structures, Vol. 43, No. 2, pp. 237-245 https://doi.org/10.1016/0045-7949(92)90140-U
  23. Doltsinis I. S. and Nolting S., 1991, 'Studies on Parallel Processing for Coupled field Problems,' Comp. Meth. in Appl. Mech. and Engrg., Vol. 89, No. 1-3, pp. 497-521
  24. El-Sayed M.E.M. and Hsiung C.K., 1994, 'Parallel Finite Element Computation with Separate Substructures,' Computers & Structures, Vol. 36, No. 2, pp. 261-265
  25. Saad Y., 1996, Iterative Methods for Sparse Linear Systems, PWS Publishing Company
  26. Blackford L.S., Choi J., et al., 1997, ScaLAPACK User's Guide, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA
  27. Geary A., Dongarra J., 1996, 'Implementation of ScaLapack of Divide-and-Conquer Algorithms for Banded and Tridiagonal Linear Systems,' Lapack Working Note
  28. Law K.H., 1986, 'A Parallel Finite Element Solution Method,' Computers & Structures, Vol. 20, No. 6, pp. 845-858 https://doi.org/10.1016/0045-7949(86)90254-3
  29. Carter W.T., Sham T.L. and Law K.H., 1989, 'A Parallel Finite Element Method and Its Prototype Implementation on a Hypercube,' Computers & Structures, Vol. 31, No. 6, pp. 921-934 https://doi.org/10.1016/0045-7949(89)90278-2