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 uncertain structural properties are modeled as interval variables with assigned lower bound and upper bound. A novel Interval Finite Element Method is formulated in the framework of the improved interval analysis via extra unitary interval, recently proposed to limit the conservatism affecting the classical interval analysis. The key idea of the novel method is to associate an extra unitary interval to each uncertain parameter in order to keep physical properties linked to the finite elements in both the assembly and solution phases. This allows one to reduce overestimation and perform standard assembly of the interval element matrices. The lower bound and upper bound of interval displacements and stresses are evaluated by applying two different strategies both based on the so-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 accuracy and efficiency of the proposed procedure.