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Feasibility Conditions in Engineering Problems 3 2 Compatibility of a system of linear inequalities

In this paper we show how the mathematical and engineering points of view are complementary and help to model real problems that can be stated as systems of linear inequalities. The Γ-algorithm, which is used to analyze the compatibility of linear systems of inequalities, is applied to solve different engineering problems involving parametric inequality constraints: a fracture mechanics problem related to numerical integration; a heat transfer problem related to the finite differences method; a classical beam problem and the Saint-Venant torsion problem. The results provide us with the feasibility conditions so that the satisfaction of the original system of linear inequality constraints can be possible.