Algebraic solution to interval equilibrium equations of truss structures

摘要

This paper considers a recently proposed interval algebraic model of linear equilibrium equations in mechanics. Based on the algebraic completion of classical interval arithmetic (called Kaucher arithmetic), this model provides much smaller ranges for the unknowns than the model based on classical interval arithmetic and fully conforms to the equilibrium principle. The general form of interval equilibrium equations for truss structures is presented. Two numerical approaches for finding the formal (algebraic) solution to the considered class of interval equilibrium equations are proposed. A methodology for adjusting interval parameters so that the equilibrium equations be completely satisfied is also presented. Numerical examples illustrate the theoretical considerations.