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Computerized Symbolic Manipulation in Structural Mechanics

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Computerized Symbolic Manipulation in Mechanics

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 343))

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Abstract

Status and some selected applications of computerized symbolic manipulation to structural mechanics problems are summarized. The applications discussed include: a) deriving the governing nonlinear differential equations for shallow shells; b) determination of the stationary conditions for variational functionals; c) application of Rayleigh-Ritz and Bubnov-Galerkin techniques; and d) generation of characteristic arrays for finite elements. The major advantages of using computerized symbolic manipulation in each of these applications are outlined. Other reported applications are discussed and future directions for research are outlined.

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References

  1. Kahrimanian, H.G.: Analytic Differentiation by a Digital Computer, M.A. Thesis, Temple University, Philadelphia, PA, May 1953.

    Google Scholar 

  2. Nolan, J.: Analytic Differentiation on a Digital Computer, M.A. Thesis, Mathematics Dept., Massachusetts Institute of Technology, Cambridge, MA, May 1953.

    Google Scholar 

  3. Boyle, A. and Caviness, B.F. (Eds.): Future Directions for Research in Symbolic Computation, Report of a Workshop on Symbolic and Algebraic Computation, April 29–30, 1988, Washington, D.C., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990.

    Google Scholar 

  4. Bau, H.H., Herbert, T. and Yovanovich, M.M. (Eds.): Symbolic Computation in Fluid Mechanics and Heat Transfer, HTD Vol. 105, AMD Vol. 97, The American Society of Mechanical Engineers, New York, 1988.

    Google Scholar 

  5. Noor, A.K., Elishakoff, I. and Hulbert, G. (Eds.): Symbolic Computations and Their Impact on Mechanics, PVP Vol. 205, The American Society of Mechanical Engineers, New York, 1990.

    Google Scholar 

  6. Pavelle, R. and Wang, P.S.: MACSYMA from F to G, Symbolic Computation, 1 (1985), 69–100.

    MathSciNet  MATH  Google Scholar 

  7. Foster, K.R. and Bau, H.H.: Symbolic manipulation programs for the personal computer, Science, 243 (1989).

    Google Scholar 

  8. Fateman, R.J.: A review of Macsyma, IEEE Trans. on Knowledge & Data Eng., 1(1) (1989), 133–145.

    Google Scholar 

  9. Simon, B.: Symbolic math software — It’s not just for mainframes anymore, PC Magazine (Aug. 1992).

    Google Scholar 

  10. Simon, B.: Comparative CAS reviews, Notices of the American Mathematical Society, 39(7) (1992), 696–706.

    Google Scholar 

  11. Abbott, P.: Maple V and Mathematica, Notices of the American Mathematical Society, 39(8) (1992), 829–837.

    Google Scholar 

  12. Fateman, R.J.: A review of Mathematica, J. Symbolic Computation, 13 (1992), 545–579.

    MathSciNet  MATH  Google Scholar 

  13. Foster, K.R.: Macsyma for windows, IEEE Spectrum, 30(4) (1993), 66.

    Google Scholar 

  14. Levi, I.M.: Symbolic algebra by computer — applications to structural mechanics, 12th AIAA/ASME Structures, Structural Dynamics and Materials Conference, Anaheim, CA, April 19–21, 1971, AIAA Paper 71–363.

    Google Scholar 

  15. Jensen, J. and Niordson, F.: Symbolic and Algebraic Manipulation Languages and Their Application in Mechanics, in: Structural Mechanics Software Series, Vol. 1, University Press of Virginia, Charlottesville, VA, 1977, 541–576.

    Google Scholar 

  16. Noor, A.K. and Andersen, C.M.: Computerized symbolic manipulation in structural mechanics — progress and potential, Computers & Structures, 10 (1979), 95–118.

    MATH  Google Scholar 

  17. Zienkiewicz, O.C. and Morgan, K.: Finite Elements and Approximation, John Wiley & Sons, New York, 1983, 85–88.

    MATH  Google Scholar 

  18. Chepurniy, N.: Evaluation of high-order polynomial triangular finite elements using FORMAC, Proc. Second Symposium on Symbolic Algebraic Manipulation, 1971, 365–371.

    Google Scholar 

  19. Pedersen, P. and Megahed, M.M.: Axisymmetric element analysis using analytical computing, Computers & Structures, 5 (1975), 241–247.

    MATH  Google Scholar 

  20. Pedersen, P.: On computer-aided analytic element analysis and the similarities of tetrahedron elements, Int. J. Numer. Meth. Eng., 11 (1977), 611–622.

    MATH  Google Scholar 

  21. Andersen, CM. and Noor, A.K.: Use of Group-Theoretic Methods in the Development of Nonlinear Shell Finite Elements, Proc. Int. Conference on Symmetry, Similarity and Group-Theoretic Meth. Mech., University of Calgary, Calgary, Canada, 1974, 533–558.

    Google Scholar 

  22. Andersen, C.M. and Noor, A.K.: A Computerized Symbolic Integration Technique for Development of Triangular and Quadrilateral Composite Shallow-Shell Finite Elements, NASA TN-D-8067, 1975.

    Google Scholar 

  23. Noor, A. K. and Andersen, C M.: Mixed isoparametric finite element models of laminated composite shells, Comp. Meth. Appl. Mech. Eng., 11 (1977), 255–280.

    MATH  Google Scholar 

  24. Korncoff, A.R. and Fenves, S.J.: Symbolic generation of finite element stiffness matrices, Computers & Structures, 10 (1979), 119–124

    MATH  Google Scholar 

  25. Noor, A.K. and Andersen, CM.: Computerized symbolic manipulation in nonlinear finite element analysis, Computers & Structures, 13 (1981), 379–403.

    MathSciNet  MATH  Google Scholar 

  26. Wang, P.W.: FINGER: A symbolic system for automatic generation of numerical programs in finite element analysis, J. Symbolic Computation, 2 (1986), 305–316.

    MATH  Google Scholar 

  27. Wang, P.W., Tan, H., Saleeb, A. and Chang, T.Y.: Code generation for hybrid mixed mode formulation in finite element analysis, Proc. ACM SYMSAC ’88 Conf., Univ. of Waterloo, Canada (1986), 45–51.

    Google Scholar 

  28. Barbier, C, Clark, P.J., Bettess, P. and Bettess, J.A.: Automatic generation of shape functions for finite element analysis using REDUCE, Eng. Comput., 7(4) (1990), 349–358.

    Google Scholar 

  29. Chang, T.Y.P. and Tan, H.Q.: Application of Symbolic Computations in Finite Element Structural Analysis, in: Symbolic Computations and Their Impact on Mechanics (Eds. A.K. Noor, I. Elishakoff, G. Hulbert), PVP Vol. 205, Proc. symposium, ASME Winter Annual Meeting, Nov. 25–30, 1990, Dallas, TX, American Society of Mechanical Engineers, New York, 1990, 205–213.

    Google Scholar 

  30. Chang, T.Y., Tan, H.Q., Zheng, D. and Yuan, M.W.: Application of symbolic method to hybrid/mixed finite elements and computer implementation, Computers & Structures, 35(4) (1990), 293–299.

    Google Scholar 

  31. Tan, H.Q., Chang, T.Y.P. and Zheng, D.: On symbolic manipulation and code generation of a hybrid three-dimensional solid element, Engineering with Computers, 7(1) (1991), 47–59.

    Google Scholar 

  32. Nagabhushanam, J., Srinivas, C.J. and Gaonkar, G.H.: Symbolic generation of elemental matrices for finite Element Analysis, Computers & Structures, 42(3) (1992), 375–380.

    MATH  Google Scholar 

  33. Sharma, N. and Wang, P.S.: The PIER parallel FEA program generator, Proc. Thirteenth Annual ASME Int. Conf. in Engineering Conf. and Exposition, San Diego, CA (1993), 295–306.

    Google Scholar 

  34. Beltzer, A.I.: Variational and Finite Element Methods — A Symbolic Computation Approach, Springer-Verlag, Berlin, 1990.

    MATH  Google Scholar 

  35. Levi, I.M. and Hoff, N. J.: Interaction Between Axisymmetric and Nonsymmetric Creep Buckling of Circular Cylindrical Shells in Axial Compression, SUDAAR Rept. No. 388, Dept. of Aeronautics and Astronautics, Stanford University, Stanford, CA, 1970.

    Google Scholar 

  36. Andersen, CM. and Noor, A.K.: Free Vibration of Laminated Composite Elliptic Plates, in: Advances in Engineering Science, Vol. 2, NASA CP-2001, 1976, 425–438.

    Google Scholar 

  37. Andersen, C. M. and Noor, A.K.: Symbolic Manipulation Techniques for Vibration Analysis of Laminated Elliptic Plates, in: Proc. 1977 MACSYMA Users’ Conference, NASA CP-2012, 1977, 161–176.

    Google Scholar 

  38. Cohen, J.: Symbolic and numerical computer analysis of the combined local and overall buckling of rectangular thin-walled columns, Comp. Meth. Appl. Mech. Eng., 7 (1976), 17–38.

    MATH  Google Scholar 

  39. Noor, A.K. and Andersen, C.M.: Application of Symbolic Computation to Geometrically Nonlinear Analysis of Curved Beams,” in: Symbolic Computations and Their Impact on Mechanics (Ed. A.K. Noor, I. Elishakoff and G. Hulbert), PVP Vol. 205, American Society of Mechanical Engineers, New York, 1990,115–148.

    Google Scholar 

  40. Tan, H.Q.: Symbolic Derivation of Material Property Matrices in Finite Element Analysis, in: Symbolic Computation in Fluid Mechanics and Heat Transfer (Eds. H.H. Bau, T. Herbert and M.M. Yovanovich), HTD Vol. 105, American Society of Mechanical Engineers, New York, 1988, 111–116.

    Google Scholar 

  41. Arnold, S.M., Tan, H.Q. and Dong, X.: Computer Simulation of the Mathematical Modeling Involved in Constitutive Equation Development: Via Symbolic Computations, NASA TM-102532, 1989.

    Google Scholar 

  42. Arnold, S.M., Tan, H.Q. and Dong, X.: Application of Symbolic Computations to the Constitutive Modeling of Structural Materials, NASA TM-103225, 1990.

    Google Scholar 

  43. Arnold, S.M., Saleeb, A.F., Tan, H.Q. and Zhang, Y.: Explicit Robust Schemes for Implementation of a Class of Principal Value-Based Constitutive Models: Symbolic and Numerical Implementation, NASA TM-106124, 1993.

    Google Scholar 

  44. Arnold, S.M. and Tan, H.Q.: Symbolic derivation of potential based constitutive equations, Comput. Mech., 6(3) (1990), 237–246.

    MATH  Google Scholar 

  45. Elishakoff, I. and Couch, B.: Nonuniform Leipholz’s column on elastic foundation -Instability study by symbolic algebra, SM Archives, 12(1) (1987), 379–389.

    Google Scholar 

  46. Elishakoff, I. and Hollkamp, J.: Computerized symbolic solution for a nonconservative system in which instability occurs by flutter in one range of a parameter and by divergence in another, Comp. Meth. Appl. Mech. Eng., 62 (1987), 27–46.

    MATH  Google Scholar 

  47. Elishakoff, I. and Wang, X.: Generalization of Smith-Herrmann problem with the aid of computerized symbolic algebra, J. Sound & Vibration, 117(3) (1987), 537–542.

    Google Scholar 

  48. Lottati, I. and Elishakoff, I.: Influence of Shear Deformation and Rotary Inertia on Flutter of a Cantilevered Beam-Exact and Symbolic Computerized Solutions, in: Refined Dynamical Theories in Beams, Plates and Shells and Their Applications (Eds. I. Elishakoff and H. Irretier), Springer-Verlag, Berlin, 1987, 261–273.

    Google Scholar 

  49. Rehak, M.L., DiMaggio, F.L., Benaroya, H. and Elishakoff, I.: Random vibrations with Macsyma, Comp. Meth. Appl. Mech. Eng., 61 (1987), 61–70.

    MathSciNet  MATH  Google Scholar 

Books and Monographs

  1. Abell, M.L. and Braselton, J.P.: Mathematica by Example, Academic Press, Boston, 1993.

    Google Scholar 

  2. Abell, M.L. and Braselton, J.P.: Differential Equations with Mathematica, Academic Press, Boston, 1993.

    MATH  Google Scholar 

  3. Abell, M.L.: The Mathematica Handbook, Academic Press, Boston, 1992.

    MATH  Google Scholar 

  4. Akritas, A.G.: Elements of Computer Algebra with Applications, Wiley, New York, 1989.

    MATH  Google Scholar 

  5. Beltzer, A.I.: Variational and Finite Element Methods — A Symbolic Computation Approach, Springer-Verlag, New York, 1990.

    MATH  Google Scholar 

  6. Blachman, N.: Mathematica, A Practical Approach, Prentice Hall, Englewood Cliffs, New Jersey, 1992.

    MATH  Google Scholar 

  7. Blachman, N.: Mathematica: Quick Reference, Version 2, Variable Symbols, Inc., 1992.

    MATH  Google Scholar 

  8. Braden, B., Krug, D.K., McCartney, P.W. and Wilkinson, S.: Discovering Calculus with Mathematica, John Wiley, New York, 1992.

    Google Scholar 

  9. Buchberger, B., Collins, G.E. and Loos, R. (Eds.): Computer Algebra: Symbolic and Algebraic Computation, Springer-Verlag, New York, 1983.

    Google Scholar 

  10. Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B. and Watt, S.M.: First Leaves: A Tutorial Introduction to MAPLE, Watcom Publications, Waterloo, Ontario, Canada, 1988.

    Google Scholar 

  11. Char, B.W., Geddes, K.O., Gonnet, G.H., Monagan, M.B. and Watt, S.M.: First Leaves: A Tutorial Introduction to Maple V, Springer-Verlag, New York, 1992.

    MATH  Google Scholar 

  12. Chudnovsky, D.V. and Jenks, R.D. (Eds.): Computer Algebra, Lecture Notes in Pure and Applied Mathematics, Vol. 113, M. Dekker, New York, 1989.

    Google Scholar 

  13. Cohen, A.M. (Ed.): Computer Algebra in Industry, John Wiley, New York, 1993.

    MATH  Google Scholar 

  14. Crandall, R.E.: Mathematica for the Sciences, Addison-Wesley, Redwood City, CA, 1991.

    Google Scholar 

  15. Davenport, J.H., Siret, Y. and Tournier, E.: Computer Algebra: Systems and Algorithms for Algebraic Computation, Academic Press, San Diego, 1988.

    MATH  Google Scholar 

  16. Derive™, A Mathematical Assistant, Software Warehouse, Inc., Honolulu, HI, 1988.

    Google Scholar 

  17. Ellis, W. and Lodi, E.: A Tutorial Introduction to Mathematica, Brooks/Cole, Monterey, CA, 1991.

    Google Scholar 

  18. Finch, J.K. and Lehmann, M.: Exploring Calculus with Mathematica, Addison-Wesley, Redwood City, CA, 1992.

    MATH  Google Scholar 

  19. Ganzha, V.G., Rudenko, V.M. and Vorozhtsov, E.V. (Eds.): Computer Algebra and Its Applications to Mechanics, Nova Science Publishers, Commack, New York, 1993.

    Google Scholar 

  20. Gaylord, R.J., Kamin, S.N. and Wellin, P.R.: Introduction to Programming with Mathematica, Springer-Verlag, New York, 1993.

    MATH  Google Scholar 

  21. Gilligan, L. and Marquardt, J.F., Sr.: Calculus and the Derive(R) Program: Experiments with the Computer, MathWare, 604 East Mumford, Urbana, IL 61801, 1990.

    Google Scholar 

  22. Glynn, J.: Exploring Math From Algebra to Calculus with Derive(R) — A Mathematical Assistant for Your Personal Computer, MathWare, 604 East Munford, Urbana, IL 61801, 1989.

    Google Scholar 

  23. Gray, T. and Glynn, J.: Exploring Mathematics with Mathematica, Addison-Wesley, Redwood City, CA, 1991.

    MATH  Google Scholar 

  24. Gray, T. and Glynn, J.: The Beginner’s Guide to Mathematica Version 2, Addison-Wesley, Redwood City, CA, 1992.

    Google Scholar 

  25. Heck, A.: The Maple Handbook, Springer-Verlag, New York, 1993.

    Google Scholar 

  26. Heck, A.: Introduction to Maple, Springer-Verlag, New York, 1993.

    MATH  Google Scholar 

  27. Heck, A.: Introduction to Maple: A Computer Algebra System, Springer-Verlag, New York, 1993.

    Google Scholar 

  28. Hearn, A.C.: REDUCE User’s Manual, The Rand Corporation, 1987.

    Google Scholar 

  29. Hearn, A.C.: REDUCE Bibliography, The Rand Corporation, 1989.

    Google Scholar 

  30. Hirota, R. and Ito, M.: Introduction to REDUCE — Doing Symbolic Computation on PC, Science sha, Tokyo (in Japanese), 1989.

    Google Scholar 

  31. Hoft, M.H.: Laboratories for Calculus I Using Mathematica, Addison-Wesley, Redwood City, CA, 1992.

    Google Scholar 

  32. Howard, J.C.: Practical Applications of Symbolic Computations, IPC Science and Technology Press, Guildford, England, 1980.

    Google Scholar 

  33. Jenks, R.D. and Sutor, R.S.: Axiom: The Scientific Computation System, Springer-Verlag, New York, 1992.

    MATH  Google Scholar 

  34. Klimov, D.M. and Rudenko, V.M.: Methods of Computer Algebra in Mechanics Problems, Izdatel’stvo Nauka, Moscow (in Russian), 1989.

    Google Scholar 

  35. Knuth, D.E.: The Art of Computer Programming, Vol. 2: Semi-Numerical Algorithms, second edition, Addison-Wesley, Reading, MA, 1981.

    Google Scholar 

  36. Koike, S.: Mathematica: Introduction to Algebraic Computation, Gijutsuhyooronsha, Tokyo, Japan (in Japanese), 1990.

    Google Scholar 

  37. Kowalik, J.S. (Ed.): Coupling Symbolic and Numerical Computing in Expert Systems, North Holland, New York, 1986.

    Google Scholar 

  38. Kowalik, J.S. and Kitzmiller, C.T. (Eds.): Coupling Symbolic and Numerical Computing in Expert Systems II, North Holland, New York, 1988.

    MATH  Google Scholar 

  39. Lipson, J.D.: Algebra and Algebraic Computing, Addison-Wesley, Reading, MA, 1981.

    MATH  Google Scholar 

  40. MACSYMA Reference Manual, Vers. 11, Symbolics, Inc., Cambridge, MA, 1985.

    Google Scholar 

  41. MACSYMA User’s Guide, Symbolics, Inc., Cambridge, MA, 1987.

    Google Scholar 

  42. Maeder, R.E.: Programming in Mathematica, Addison-Wesley, Redwood City, CA, 1991.

    Google Scholar 

  43. Mignotte, M.: Mathématiques Pour le Calcul Formel, Presses Universitaires de France, Paris, 1989.

    MATH  Google Scholar 

  44. Nakamura, H. and Matsui, S.: Symbolic computation in Structural Mechanics Using REDUCE, Gihodo Shuppan, Tokyo (in Japanese), 1989.

    Google Scholar 

  45. Ochiai, M. and Nagatomo, K.: Linear Algebra Using REDUCE, Kindai Kagaku sha, Tokyo (in Japanese), 1990.

    Google Scholar 

  46. Pavelle, R. (Ed.): Applications of Computer Algebra, Kluwer Academic Publishers, Boston, MA, 1985.

    Google Scholar 

  47. Rand, R.H.: Computer Algebra in Applied Mathematics: An Introduction to MACSYMA, Research Notes in Mathematics, Vol. 94, Pitman Publishing, Boston, MA, 1984.

    Google Scholar 

  48. Rand, R.H. and Armbruster, D.: Perturbation Methods, Bifurcation Theory and Computer Algebra, Springer-Verlag, New York, 1987.

    MATH  Google Scholar 

  49. Rayna, G.: REDUCE: Software for Algebraic Computation, Springer-Verlag, New York, 1987.

    MATH  Google Scholar 

  50. Redfern : The Maple Handbook, Springer-Verlag, New York, 1993.

    MATH  Google Scholar 

  51. Rehak, M.L., Dimaggio, F.L., Benaroya, H. and Elishakoff, I.: Random Vibrations with MACSYMA, Comput. Meth. Appl. Mech. and Eng., 61, 1987, 61–70.

    MathSciNet  MATH  Google Scholar 

  52. Rice, J.R.: Mathematical Aspects of Scientific Software, IMA Volumes in Mathematics and Its Applications, Springer-Verlag, New York, 1988.

    Google Scholar 

  53. Skeel, R.D. and Keiper, J.B.: Elementary Numerical Computing with Mathematica, McGraw-Hill, New York, 1993.

    Google Scholar 

  54. Skiena, S.S.: Implementing Discrete Mathematics: Combinatories and Graph Theory with Mathematica, Addison-Wesley, Redwood City, CA, 1991.

    Google Scholar 

  55. Sims, C.C.: Abstract Algebra: A Computational Approach, John Wiley and Sons, New York, 1984.

    MATH  Google Scholar 

  56. Stauffer, D., Hehl, F.W., Winkelmann, V. and Zabolitzky, J.G.: Computer Simulation and Computer Algebra, Lectures for Beginners, Springer-Verlag, New York, 1989.

    Google Scholar 

  57. Stroyan, K.D.: Scientific Projects and Mathematical Background for Calculus Using Mathematica, Academic Press, Boston, 1993.

    Google Scholar 

  58. Symbolics, Bibliography of Publications Referencing MACSYMA: Computer Aided Mathematics Group, Eleven Cambridge Center, Cambridge, MA 02142, 1987.

    Google Scholar 

  59. Touretzky, D.S.: LISP: A Gentle Introduction to Symbolic Computation, Harper & Row, New York, 1984.

    Google Scholar 

  60. Tournier, E.: Computer Algebra and Differential Equations, Computational Mathematics and Applications, Academic Press, 1990.

    Google Scholar 

  61. Vardi, I.: Computational Recreations in Mathematica, Addison-Wesley, Redwood City, CA, 1991.

    MATH  Google Scholar 

  62. Vvedensky, D.: Partial Differential Equations with Mathematica, Addison-Wesley, Redwood City, CA, 1993.

    MATH  Google Scholar 

  63. Wade, E. and Lodi, E.: A Tutorial Introduction to Mathematica, Brooks/Cole, 1991.

    Google Scholar 

  64. Wagon, S.: Mathematica in Action, W.H. Freeman, San Francisco, CA, 1990.

    Google Scholar 

  65. Wickham-Jones: Computer Graphics with Mathematica, Springer-Verlag, New York.

    Google Scholar 

  66. Wolfram, S.: Mathematica: A System for Doing Mathematics by Computer, Addison-Wesley, Redwood City, CA, 1991.

    Google Scholar 

  67. Wolfram, S.: Mathematica Reference Guide, Addison-Wesley, Redwood City, CA, 1992.

    Google Scholar 

  68. Wooff, C. and Hodgkinson, D.: muMath: A Microcomputer Algebra System, Academic Press, London, 1987.

    MATH  Google Scholar 

  69. Zimmer, H.G.: Computational Problems, Methods and Results in Algebraic Number Theory, Lecture Notes in Mathematics, Vol. 268, Springer-Verlag, New York, 1972.

    Google Scholar 

Conference Proceedings

  1. Symbolic Languages in Data Processing, Proc. of a Symposium organized by Int. Computation Centre, Rome, March 26–31, 1962, Gordon & Breach Science, New York, 1962.

    Google Scholar 

  2. Petrick, S.R. (Ed.): Proc. Second Symposium on Symbolic and Algebraic Manipulation, March 23–25, 1971, Los Angeles, CA, Association for Computing Machinery, New York, 1971.

    Google Scholar 

  3. Jenks, R.D. (Ed.): Symsac 76: Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation, Aug. 10–12, 1976, Yorktown Heights, New York, Association for Computing Machinery, New York, 1976.

    Google Scholar 

  4. Jenks, R.D. (Ed.): Symsac 76: Proc. 1976 ACM Symposium on Symbolic and Algebraic Computation, Aug. 10–12, 1976, Yorktown Heights, New York, Association for Computing Machinery, New York, 1976.

    Google Scholar 

  5. Proc. 1977 MACS YMA User’s Conference, University of California, Berkeley, July 27–29 1977 NASA CP-2012.

    Google Scholar 

  6. Lewis, V.E. (Ed.): Proc. 1979 MACSYMA User’s Conference, Washington, D.C., June 20–22, 1979.

    Google Scholar 

  7. Ng, E.W. (Ed.): Symbolic and Algebraic Computation: EUROSAM 79, International Symposium on Symbolic and Algebraic Manipulation, June 1979, Marseille, France, Springer-Verlag, Berlin, 1979.

    Google Scholar 

  8. Wang, P.S. (Ed.): Symsac ’81: Proc. 1981 ACM Symposium on Symbolic and Algebraic Computation, Aug. 5–7, 1981, Snowbird, UT, Association for Computing Machinery, New York, 1981.

    Google Scholar 

  9. Calmet, J. (Ed.): Computer Algebra: EUROCAM 82 European Computer Algebra Conference, Marseille, France, April 5–7, 1982, Lecture Notes in Computer Science, No. 144, Springer-Verlag, Berlin, 1982.

    Google Scholar 

  10. Buchberger, B., Collins, G.E. and Loos, R.G.K. (Eds.): Computer Algebra: Symbolic and Algebraic Computation, second edition, Springer-Verlag, Wien, 1983.

    Google Scholar 

  11. van Hulzen, J.A. (Ed.): Computer Algebra: EUROCAL’83, European Computer Algebra Conference, London, England, March 28–30, 1983, Lecture Notes in Computer Science, No. 162, Springer-Verlag, Berlin, 1983.

    MATH  Google Scholar 

  12. Atkinson, M.A.: Computational Group Theory, Proc. London Mathematical Society Symposium on Computational Group Theory, Academic Press, San Diego, 1984.

    Google Scholar 

  13. Fitch, J. (Ed.): EUROSAM 84, Int. Symposium on Symbolic and Algebraic Computation, Proc. Symposium, July 9–11, 1984, Cambridge, England, Lecture Notes in Computer Science, No. 174, Springer-Verlag, 1984.

    Google Scholar 

  14. Golden, V.E. (Ed.): Proc. 1984 MACSYMA User’s Conference, Schenectady, NY, July 23–25, 1984, General Electric, Schenectady, New York, 1984.

    Google Scholar 

  15. Hitotumatu, S. (chairman): Fifth RIMS Conference on Formula Manipulation and Its Application to Mathematical Study, Kyoto, Japan, 1985.

    Google Scholar 

  16. Inada, N. and Soma, T. (Eds.): Proc. of the Second RIKEN Int. Symposium on Symbolic and Algebraic Computation by Computers, Wako-shi, Japan, Series in Computer Science, Vol. 2, World Scientific Publishers, Philadelphia, PA, 1985.

    Google Scholar 

  17. Pavelle, R. (Ed.): Applications of Computer Algebra (papers based on the proc. Symposium on Symbolic Algebraic Manipulation in Scientific Computation presented by the ACS Division of Computers in Chemistry), 188th Meeting of the American Chemical Society, Aug. 26–31, 1984, Kluwer Academic Publishers, Boston, MA, 1985.

    Google Scholar 

  18. Carr, B.W. (Ed.): Symsac ’86: Proc. 1986 Symposium on Symbolic and Algebraic Computation, July 21–23, 1986, Waterloo, Ontario, Canada, Association for Computing Machinery, New York, 1986.

    Google Scholar 

  19. Char, B.W. (Ed.): Symsac ’86: Proc. 1986 ACM Symposium on Symbolic and Algebraic Computation, July 21–23, 1986, Waterloo, Ontario, Association for Computing Machinery, Baltimore, Maryland, 1986.

    Google Scholar 

  20. Caviness, B.F. (Ed.): EUROCAL ’85, Proc. European Conference on Computer Algebra, April 1–3, 1985, Linz, Austria, Vol. 2, Research Contributions, Lecture Notes in Computer Science No. 203–204, Springer-Verlag, Berlin, 1986.

    Google Scholar 

  21. Buchberger, B. (Ed.): EUROCAL ’85, Proc. European Conference on Computer Algebra, April 1–3, 1985, Linz, Austria, Vol. 1, Invited Lectures, Lecture Notes in Computer Science, No. 203–204, Springer-Verlag, Berlin, 1986.

    Google Scholar 

  22. Janssen, R. (Ed.): Trends in Computer Algebra, Proc. Int. Symposium, Bad Neuenahr, May 19–21, 1987, Lecture Notes in Computer Science, Vol. 296, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  23. Bau, H.H., Herbert T. and Yovanovich, M.M. (Eds.): Symbolic Computations in Fluid Mechanics and Heat Transfer, Proc. symposium, ASME Winter Annual Meeting, Nov. 27-Dec, 2, 1988, Chicago, IL, HTD Vol. 105, AMD Vol. 97, ASME, New York, 1988.

    Google Scholar 

  24. Delia Dora, J. and Fitch, J. (Eds.): CAP-88, Proc. Workshop on Computer Algebra and Parallelism, University of Grenoble, France, June 1988, Academic Press, London, 1988.

    Google Scholar 

  25. Gianni, P. (Ed.): Symbolic and Algebraic Computation: Int. Symposium ISSAC ’88, Rome, July 4–8, 1988, Springer-Verlag, Berlin, 1988.

    Google Scholar 

  26. Miola, A. (Ed.): ISSAC ’88, 1988 Int. Symposium on Symbolic and Algebraic Computation, Rome, Lecture Notes in Computer Science, No. 358, Springer-Verlag, 1988.

    Google Scholar 

  27. Davenport, J.H. (Ed.): EUROCAL ’87, Proc. European Conference on Computer Algebra, June 1987, Leipzig, West Germany, Lecture Notes in Computer Science No. 378, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  28. Grossman, R. (Ed.): Symbolic Computation: Applications to Scientific Computing, Proc. Conference on Symbolic Computation, Moffett Field, CA, Jan. 15–16, 1987, Society for Industrial and Applied Mathematics, Philadelphia, PA, Vol. 5,1989.

    Google Scholar 

  29. Proc. ACM-SIGSAM 1989 Int. Symposium on Symbolic and Algebraic Computation, July 17–19, 1989, Portland, OR, ACM Press, 1989.

    Google Scholar 

  30. Boyle, A. and Caviness, B.F. (Eds.): Future Directions for Research in Symbolic Computation, Report of a Workshop on Symbolic Computation, April 29–30, 1988, Washington, D.C., Society for Industrial and Applied Mathematics, Philadelphia, PA, 1990.

    Google Scholar 

  31. ISSAC ’90, Proc. Int. Symposium on Symbolic and Algebraic Computation, Tokyo, Japan, ACM Press/Addison Wesley, 1990.

    Google Scholar 

  32. Miola, C.A. (Ed.): DISCO ’90, Proc. Symposium on Design and Implementation of Symbolic Computation Systems, April 10–12, 1990, Capri, Italy, Lecture Notes in Computer Science, Vol. 429, Springer-Verlag, Berlin, 1990.

    Google Scholar 

  33. Noor, A.K., Elishakoff, I. and Hulbert, G. (Eds.): Symbolic Computations and Their Impact on Mechanics, Proc. of an ASME Symposium, Nov. 25–30, 1990, Dallas, TX, PVP Vol. 205, ASME, New York, 1990.

    Google Scholar 

  34. Qingsheng, T.: Symbolic and Algebraic Manipulation for Formulae of Interpolation and Quadrature, ISSAC ’90; Proc. Int. Symposium on Symbolic and Algebraic Computation, Aug. 20–24, 1990, Tokyo, Japan, Association for Computing Machinery, New York, 1990.

    Google Scholar 

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  1. University of Virginia, Hampton, VA, USA

    A. K. Noor

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  1. Technical University of Hamburg, Harburg, Germany

    E. Kreuzer

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© 1994 Springer-Verlag Wien

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Noor, A.K. (1994). Computerized Symbolic Manipulation in Structural Mechanics. In: Kreuzer, E. (eds) Computerized Symbolic Manipulation in Mechanics. CISM International Centre for Mechanical Sciences, vol 343. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3010-0_3

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  • DOI: https://doi.org/10.1007/978-3-7091-3010-0_3

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