Computer-based manipulation of systems of equations in elasticity problems with Gröbner bases. (English) Zbl 0847.73075
Summary: The classical method of Buchberger’s Gröbner bases for multivariate polynomial equations with a variety of applications in computer algebra is applied to three problems in elasticity concerning (i) a simple elastic truss, (ii) an elementary plane elasticity problem in rectangular coordinates, and (iii) the derivation of a compatibility partial differential equation for the stress components and the proof of biharmonicity of the same components also in plane elasticity. The present results aim at the practical illustration of the possibility of deriving computer-generated formulae in elasticity problems by using Gröbner bases (as has been done in the case of geometric problems), and the popular and modern computer algebra system Maple V (equipped with a related package) has been used. Further generalizations of the present results are quite possible and some of these are discussed in brief.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74B99 | Elastic materials |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
equation for stress components; multivariate polynomial equations; simple elastic truss; plane elasticity problem; proof of biharmonicity; computer algebra system Maple VReferences:
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