Sharp Bounds for Strains and Stresses in Uncertain Mechanical Models ⋆

Abstract. Many mechanical systems, involving interval uncertainties and modelled by finite element method, can be described by parameter dependent systems of linear interval equations and response quantities depending on the system solution. A newly developed hybrid interval approach for solving parametric interval linear systems is applied to a 2D engineering model with interval parameters and the results are compared to other interval methods. A new technique providing very sharp bounds for the response quantities, such as element strains and stresses, is developed. The sources for overestimation when dealing with interval computations are demonstrated on a numerical plain strain example.

Sharp Bounds for Strains and Stresses in Uncertain Mechanical Models ⋆

Abstract. Many mechanical systems, involving interval uncertainties and modelled by finite element method, can be described by parameter dependent systems of linear interval equations and response quantities depending on the system solution. A newly developed hybrid interval approach for solving parametric interval linear systems is applied to a 2D engineering model with interval parameters and the results are compared to other interval methods. A new technique providing very sharp bounds for the response quantities, such as element strains and stresses, is developed. The sources for overestimation when dealing with interval computations are demonstrated on a numerical plain strain example.