A system for the symbolic analysis of problems in engineering mechanics

ABSTRACT

In this paper, we present a system for the symbolic solution of problems in engineering mechanics. Of critical importance is a sub-system for maintaining and manipulating quantities containing unevaluated intermediate variables. Without this subsystem, intermediate expression expansion makes symbolic mechanics impractical for all but trivial problems. With the subsystem, readable symbolic solutions may be derived for mechanics problems of textbook complexity and above. More complex symbolic solutions in a form amenable to code generation may be derived for mechanics problems of the complexity found in a practical engineering context.

REFERENCES

• 1: Shang-Ching Chou, A method for the mechanical derivation of formulas in elementary geometry, Journal of Automated Reasoning, v.3 n.3, p.291-299, Sept. 1987
• 2: S.-C. Chou, Mechanical geometry theorem proving, Kluwer Academic Publishers, Norwell, MA, 1987
• 3: Shang Chou , Xiao Gao, Automated Reasoning in Mechanics Using Ritt-wu''s Method, University of Texas at Austin, Austin, TX, 1989
• 4: B. Kutzler , S. Stifter, Automated geometry theorem proving using Buchberger's algorithm, Proceedings of the fifth ACM symposium on Symbolic and algebraic computation, p.209-214, July 21-23, 1986, Waterloo, Ontario, Canada [doi>10.1145/32439.32480]
• 5: P. H. Todd , George W. Cherry, Symbolic Analysis of Planar Drawings, Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation, p.344-355, July 04-08, 1988
• 6: Philip Todd, A k-tree generalization that characterized consistency of dimensioned engineering drawings, SIAM Journal on Discrete Mathematics, v.2 n.2, p.255-261, May 1989 [doi>10.1137/0402022]
• 7: Todd P. (1992) "A Constructive Vaxiational Geometry Based Mechanism Design Software Package" ASME DE-Vo146, Mechanism Design & Synthesis, pp 267 - 273.
• 8: Todd P. and Kcmpcr H. (1993) Analytix Version 2.0 Users' Manual, Saltire Software, Beaverton OR.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.0 General

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Engineering

General Terms:
Algorithms, Theory, Verification