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Inelastic vector finite element analysis of RC shells

  • Min, Chang-Shik (Department of Ocean and Civil Engineering, Cheju National University) ;
  • Gupta, Ajaya Kumar (Center for Nuclear Power Plant Structures, Equipment and Piping, North Carolina State University)
  • 발행 : 1996.03.25

초록

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.

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참고문헌

  1. Agrawal, O. P., Danhof, K.J. and Kumar, R. (1994), "A superelement model based parallel algorithm for vehicle dynamics." Computers & Structures, 51(4), 411-423. https://doi.org/10.1016/0045-7949(94)90326-3
  2. Akbar, Habibollah, and Gupta, Ajaya Kumar (1985), "Membrane reinforcement in concrete shells: design versus nonlinear behavior," North Carolina State University, Raleigh, North Carolina 27695-7908, January, Reinforced Concrete Shell Research Report.
  3. Akbar, Habibollah, and Gupta, Ajaya Kumar (1986), "Ultimate behavior of an R.C. nuclear containment subjected to internal pressure and earthquake," J. Struct. Engrg., ASCE, 112(6), June, 1280-1295. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:6(1280)
  4. Barragy, E., Carey, G. F., and Geijn, R.Van De. (1994), "Performance and scalability of finite element analysis for distributed parallel computation." J. of Parallel and Distributed Computing, 21(2), 202-212. https://doi.org/10.1006/jpdc.1994.1052
  5. Cray SR-0018 C, CFT77 reference manual, SR-0018 C, Cray Research, Inc.
  6. Cray SR-2040 6.0, UNICOS performance utilities reference manual, Cray Research, Inc.
  7. Cray SR-2081 6.0, UNICOS math and scientific library reference manual, Cray Research, Inc.
  8. Dongarra, J.J., Moler, C.B., Bunch, J.R., and Stewart, G.W. (1979), LINPACK Users Guide, Society for Industrial and Applied Mathematics (SIAM).
  9. Dongarra, J. J., Gustavson, F. G., and Karp, A. (1984a), "Implementing linear algebra algorithms for dense matrices on a vector pipeline machine," SIAM Review, 26(1), January, 91-112. https://doi.org/10.1137/1026003
  10. Dongarra, Jack, J., and Eisenstat, Stanley C. (1984b), "Squeezing the most out of an algorithm in Cray FORTRAM." ACM Transactions on Mathematical Software, 10(30), 219-230. https://doi.org/10.1145/1271.319413
  11. Dongarra, J., Kennedy, K., Messina, P., Sorensen, D. C., and Voigt, R. (1992), Parallel processing for scientific computing, Proceedings of the fifth SIAM conference, March 25-27, 1991, in Houston, Tex.
  12. Golub, Gene and Ortega, James M., (1993), Scientific computing - An introduction with parallel computing, Academic Press, Inc., San Diago, CA 92101-4311.
  13. Gupta, A.K., and Maestrini, S. (1986), "Investigation of hyperbolic cooling tower ultimate behavior," Engrg. Struct., 8, April, 87-92. https://doi.org/10.1016/0141-0296(86)90024-6
  14. Hand, Frank R., Pecknold, David A. and Schnobrich, William C. (1973), "Nonlinear layered analysis of RC plates and shells," J. Struct. Div., ASCE, 99(7), 1491-1505.
  15. Hutchinson, S., Hensel, E., Castillo, S., and Dalton, K. (1991), "The Finite element solution of elliptical systems on a data parallel computer," Int. J. for Numer. Methods in Engrg., 32, 347-362. https://doi.org/10.1002/nme.1620320208
  16. IBM. Corporation (1987), IBM Engineering and Scientific Subroutine Library: Guide and Reference, 2 edition, September. Program number: 5668-863.
  17. Lambiotte, Jules J. (1975), The Solution of linear systems of equations on a vector computer. Ph. D. thesis, University of Virginia.
  18. Levesque, John M., and Williamson, Joel W. (1989), A guidebook of Fortran on supercomputers, Academic Press, Inc., San Diego, California 92101.
  19. Lin, Cheng-Shung, and Scordelis, Alexander C. (1975), "Nonlinear analysis of RC shells of general form," J. Struct. Div., ASCE, 101(3), 523-538.
  20. Mahmoud, Bahaa Eldin H., and Gupta, Ajaya Kumar. (1993), "Inelastic large displacement behavior and buckling of hyperbolic cooling tower shells." Center for nuclear Power Plant Structures, Equipment and Piping, North Carolina State University, Raleigh, North Carolina 27695-7908. May, Report.
  21. Mang, H. A., Floegl, H., Trappel, F., and Walter, H. (1983), "Wind-loaded reinforced-concrete cooling towers: buckling or ultimate load?" Engrg. Struct., 5 July, 163-180. https://doi.org/10.1016/0141-0296(83)90014-7
  22. Milford, R. V. and Schnobrich, W. C. (1984), "Nonlinear behavior of reinforced concrete cooling towers," Technical report, University of Illinois, Urbana-Champaign, Illinois 61801, May. Structural Research Series, 514.
  23. Min, Chang-Shik, and Gupta, Ajaya Kumar (1991), "Vector finite-element analysis using IBM 3090-600EVF," Commun. in Applied Numer. Methods, 7(2), 155-164. https://doi.org/10.1002/cnm.1630070209
  24. Min, Chang-Shik and Gupta, Ajaya Kumar. (1992), "A study of inelastic behavior of reinforced concrete shells using supercomputers." Department of Civil Engrg., North Carolina State University, Raleigh, North Carolina 27695-7908. March. Reinfored Concrete Shell Research Report,
  25. Min, Chang Shik, and Gupta, Ajaya Kumar. (1993), "Inelastic behavior of hyperbolic cooling tower." J. of Struct. Engrg., ASCE, 119(7), July, 2235-2255. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(2235)
  26. Min, Chang-Shik, and Gupta, Ajaya Kimar. (1994a), "Vector algorithm for reinforced concrete shell element stiffness matrix," Structural Engineering and Mechanics, An International Journal, 2(2), 125-139. https://doi.org/10.12989/sem.1994.2.2.125
  27. Min, Chang-Shik, and Gupta, Ajaya Kimar (1994b), "Vector algorithm for layered reinforced concrete shell element stiffness matrix," Center for Nuclear Power Plant Structures, Equipment and Piping, North Carolina State University, Raleigh, North Carolina 27695-7908. April. Report.
  28. Min, Chang Shik, and Gupta, Ajaya Kumar (1994c), "Inelastic behavior of reinforced concrete hyperbolic paraboloid saddle shell," Engrg. Struct., 16(4), 227-2375. https://doi.org/10.1016/0141-0296(94)90061-2
  29. Min, Chang Shik, and Gupta, Ajaya Kumar (1995), "Vector algorithm for layered reinforced concrete shell element stiffness matrix," Structural Engineering and Mechanics, An International Journal, 3(2), 173-183. https://doi.org/10.12989/sem.1995.3.2.173
  30. Noor, Ahmed K., and Peters, Jeanne M. (1986), "Element stiffness computation on CDC Cyber 205 computer." Commun. in Applied Numer. Methods, 2, 317-328. https://doi.org/10.1002/cnm.1630020314
  31. Ortega, James M., (1988), Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press, New York, N.Y. 10013.
  32. Silvester, D.J. (1988), "Optimizing finite element matrix calculation using the general technique of element vectorization," Parallel Computing, 6, 157-164. https://doi.org/10.1016/0167-8191(88)90081-6
  33. Storaasli, O.O., Nguyen, D.T., and Agrawal, T. K. (1989), "Parallel-vector solution of large-scale structural analysis problems on supercomputers," In 30th Structures, Structural Dynamics and Material Conference, 859-867. Mobile, Alabama, April, AIAA/ASME/ASCE/AHS/ASC.
  34. Yagawa, G., Yoshioka, A., Yoshimura, S., and Soneda, N. (1993), "A parallel finite element method with a supercomputer network," Computers & Structures, 47(3), 407-418. https://doi.org/10.1016/0045-7949(93)90236-7

피인용 문헌

  1. Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999) vol.17, pp.3, 2000, https://doi.org/10.1108/02644400010324893
  2. Design and inelastic behavior of hyperbolic cooling tower vol.5, pp.4, 2001, https://doi.org/10.1007/BF02829106
  3. Ultimate behavior of RC hyperbolic paraboloid saddle shell vol.5, pp.5, 1997, https://doi.org/10.12989/sem.1997.5.5.507
  4. Design and ultimate behavior of RC plates and shells: two case studies vol.14, pp.2, 2002, https://doi.org/10.12989/sem.2002.14.2.171
  5. Limits to the strength design of reinforced concrete shells and slabs vol.61, 2014, https://doi.org/10.1016/j.engstruct.2014.01.011
  6. Design and ultimate behavior of RC plates and shells vol.228, pp.1-3, 2004, https://doi.org/10.1016/j.nucengdes.2003.06.023