A novel Interval Finite Element Method based on the improved interval analysis

Static analysis of linear–elastic structures with uncertain parameters subjected to deterministic loads is addressed. The uncertainstructural properties are modeled as interval variables with assigned lower bound and upper bound. A novel Interval Finite ElementMethod is formulated in the framework of the improved interval analysis via extra unitary interval, recently proposed to limit theconservatism affecting the classical interval analysis. The key idea of the novel method is to associate an extra unitary intervalto each uncertain parameter in order to keep physical properties linked to the finite elements in both the assembly and solutionphases. This allows one to reduce overestimation and perform standard assembly of the interval element matrices. The lowerbound and upper bound of interval displacements and stresses are evaluated by applying two different strategies both based on theso-called Interval Rational Series Expansion for deriving the approximate explicit inverse of the interval global stiffness matrix.Numerical examples concerning 2D and 3D structures with uncertain Young’s modulus are presented to demonstrate the accuracyand efficiency of the proposed procedure.