Interval algebraic approach to equilibrium equations in mechanics

Abstract

The engineering demand for more realistic and accurate models involving interval uncertainties lead to a new interval model of linear equilibrium equations in mechanics, which is based on the algebraic completion of classical interval arithmetic (called Kaucher arithmetic). Interval algebraic approach consists of three parts: representation convention, computing algebraic solution and result interpretation. The proposed approach replaces straightforward a deterministic model by an interval model in terms of proper and improper intervals, fully conforms to the equilibrium principle and provides sharper enclosure of the unknown quantities than the best known methods based on classical interval arithmetic. Numerical applications described by systems of linear interval equilibrium equations where the number of the unknowns is equal to the number of the equations are considered in details.