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On the Analytical and Numerical Computation in Mechanical Modeling

  • Marcel Migdalovici
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 28)

Abstract

In the paper are studied the possibilities of replacing the manual analytical calculation, which intervenes in the mechanical modeling, by an isomorphic numerical calculation which can be performed on digital computers. An algorithm is described for performing the greatest common divisor of two polynomials with several variables that may be used to determine the analytical inverse matrix for a matrix of such polynomials that are used in a mathematical modeling of mechanical phenomena. A new definition of the Euclidean ring is proposed. The question of how much can lead the formal (analytical) calculation in the modeling up to replacing with a numerical method of solution calculation is emphasized.

Keywords

Thin Plate Fundamental Form Integral Domain Product Operation Great Common Divisor 
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References

  1. 1.
    Buchberger B, Collins GE, Loos R (1982) Symbolic & algebraic computation. Computing supplementum 4. Springer–Verlag, Wien-New YorkMATHGoogle Scholar
  2. 2.
    Davenport J, Siret Y, Tournier E (1987) Formal calculus (in French). Masson, Paris, New York, Barcelone, Milan, Mexico, Sao PauloGoogle Scholar
  3. 3.
    Goldenveizer AL (1953) Theory of elastic shells (in Russian). Gostehizdat, MoscowGoogle Scholar
  4. 4.
    Ion D Ion, Nita C, Nastasescu C (1984) Complements of algèbra (in Romanian). Scientific and Encyclopaedic Publishing House, BucharestGoogle Scholar
  5. 5.
    Iovanescu VR (1980) Stress in shells with middle surface of mixed type (in Romanian). Ph.D. thesis, Bucharest UniversityGoogle Scholar
  6. 6.
    Jacobson N (1973) Basic algebra vol I. Freeman, San FranciscoGoogle Scholar
  7. 7.
    Knuth DE (1981) The art of computer programming vol II seminumerical algorithms. Addison–WesleyGoogle Scholar
  8. 8.
    Migdalovici M (1985) Automation of mechanical structures calculus with application to nuclear power plant (in Romanian). Ph.D. thesis, Bucharest UniversityGoogle Scholar
  9. 9.
    Migdalovici M (2004) A theorem of division with a remainder in a set of polynomials with several variables. Creative Math 13:5–10MathSciNetGoogle Scholar
  10. 10.
    Nastasescu C, Nita C, Vraciu C (1986) Basic algebra vol I (in Romanian). Publishing House of the Romanian Academy, BucharestGoogle Scholar
  11. 11.
    Visarion V, Migdalovici M (1979) On the transposition of the analytical calculation on computers. Rev Roum Sci Techn Mec Appl 24:847–853MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Marcel Migdalovici
    • 1
  1. 1.Romanian AcademyInstitute of Solid Mechanics 15Romania

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