Structural Engineering and Mechanics

  • 제5권5호
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  • Pages.635-644
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  • 1997
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Parallel computation for transcendental structural eigenproblems

  • Kennedy, D. (Cardiff School of Engineering, University of Wales Cardiff) ;
  • Williams, F.W. (Cardiff School of Engineering, University of Wales Cardiff)
  • 발행 : 1997.09.25
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초록

The paper reviews the implementation and evaluation of exact methods for the computation of transcendental structural eigenvalues, i.e., critical buckling loads and natural frequencies of undamped vibration, on multiple instruction, multiple data parallel computers with distributed memory. Coarse, medium and fine grain parallel methods are described with illustrative examples. The methods are compared and combined into hybrid methods whose performance can be predicted from that of the component methods individually. An indication is given of how performance indicators can be presented in a generic form rather than being specific to one particular parallel computer. Current extensions to permit parallel optimum design of structures are outlined.

키워드

참고문헌

  1. An, W., Watkins, W.J., Kennedy, D. and Williams, F.W. (1997a), "Parallel critical buckling calculations for prismatic plate assembly" submitted for publication.
  2. An, W., Watkins, W.J., Kennedy, D. and Williams, F.W. (1997b), "Parallel substructuring in exact eigenvacalculations for prismatic plate assembly", in preparation
  3. Anderson, M.S. and Williams, F.W. (1987), "BUNVIS-RG: exact frame buckling and vibration program, with repetitive geometry and substructuring", J. Spacecr. Rockets, 24(4), 353-361. https://doi.org/10.2514/3.25924
  4. Chan, K.L., Kennedy, D. and Williams, F.W. (1997a), "Efficient parallel bounding solution method for structural transcendental eigenvalue problems", submitted for publication.
  5. Chan, K.L., Kennedy, D. and Williams, F.W. (1997b), "Parallel design methods for optimising lightweight structures", to be presented at the Mouchel Centenary Conference on Innovation in Civil and Structural Engineering, Cambridge, U.K.
  6. Hopper, C.T., Simpson, A. and Williams, F.W. (1980), "A study of the bounds on eigenvalues of a transcendental stiffness matrix provided by a simply derived linear matrix pencil", J. Struct. Mech., 8(4), 365-422. https://doi.org/10.1080/03601218008907369
  7. Kennedy, D. (1994), "Efficient computation of transcendental structural eigenvalues using exact member stiffnesses", PhD Thesis, University of Wales, U.K.
  8. Kennedy, D., Watkins, W.J. and Williams, F.W. (1995), "Hybrid parallel computation of transcendental structural eigenvalues", AIAA J., 33(11), 2194-2198. https://doi.org/10.2514/3.12966
  9. Watkins, W.J., Kennedy, D. and Williams, F.W. (1996), "Efficient parallel solution of structural eigenvalue problems", Adv. Eng. Software, 25(2/3), 281-289. https://doi.org/10.1016/0965-9978(95)00094-1
  10. Watkins, W.J., Kennedy, D. and Williams, F.W. (1997a), "Efficient parallel Gauss-Doolittle matrix triangulation", Comput. Struct., 62(1), 185-195. https://doi.org/10.1016/S0045-7949(96)00282-9
  11. Watkins, W.J., Kennedy, D. and Williams, F.W. (1997b), "On estimating machine dependency of fine and coarse-grained parallel structural computations", Microcomp. in Civil Eng., 12(2), 119-128. https://doi.org/10.1111/0885-9507.00050
  12. Williams, F.W. (1973), "Comparison between sparse matrix and substructure methods", Int. J. Num. Methods Eng., 5(3), 383-394. https://doi.org/10.1002/nme.1620050309
  13. Williams, F.W. and Kennedy, D. (1988a), "Fast Gauss-Doolittle matrix triangulation", Comput. Struct, 28(2), 143-148. https://doi.org/10.1016/0045-7949(88)90033-8
  14. Williams, F.W. and Kennedy, D. (1988b), "Reliable use of determinants to solve non-linear structural eigenvalue problems efficiently", Int. J. Num. Methods Eng., 26(8), 1825-1841. https://doi.org/10.1002/nme.1620260810
  15. Williams, F.W., Kennedy, D.. Butler, R. and Anderson, M.S. (1991), "VICONOPT: program for exact vibration and buckling analysis or design of prismatic plate assemblies", AIAA J., 29(11), 1927-1928. https://doi.org/10.2514/3.10820
  16. Wittrick, W.H. and Williams, F.W. (1971), "A general algorithm for computing natural frequencies of elastic structures", Q. J. Mech. Appl. Math., 24(3), 263-284. https://doi.org/10.1093/qjmam/24.3.263
  17. Zabinsky, Z.B., Smith, R.L., McDonald, J.F., Romeijn, H.E. and Kaufman, D.E. (1993), "Improving hit-and-run for global optimization", J. Global Opt., 3(2), 171-192. https://doi.org/10.1007/BF01096737