Derivation of feasibility conditions in engineering problems under parametric inequality constraints with classical Fourier elimination

Abstract

Fourier (or Motzkin or even Fourier–Motzkin) elimination is the classical and equally old analogue of Gaussian elimination for the solution of linear equations to the case of linear inequalities. Here this approach (and two standard improvements) is applied to two engineering problems (involving numerical integration in fracture mechanics as well as finite differences in heat transfer in the parametric case) with linear inequality constraints. The results (solvent systems of inequalities including only the related parameters) concern the feasibility conditions (existential quantifier-free formulae) so that the satisfaction of the original system of linear inequality constraints can be possible (for appropriate values of the variables in it). Further applications, e.g. to singular integral equations and to the boundary and finite element techniques in computational mechanics and engineering, are also possible. The computer algebra system Maple V has been used and a related elementary procedure for Fourier elimination was prepared and is displayed. The competitive Weispfenning elimination approach can also be used instead. The present results constitute an extension of the already available applications of computer algebra software to the classical approximate–numerical methods traditionally employed in engineering and are also related to computational quantifier elimination techniques in computer algebra and applied logic. Copyright © 2000 John Wiley & Sons, Ltd.