An interval finite element method for the analysis of structures with spatially varying uncertainties. (February 2019) - Sofi, Alba; Romeo, Eugenia; Barrera, Olga; Cocks, Alan
Highlights: Finite element analysis of linear-elastic structures with spatially varying uncertainties is addressed. Spatially varying uncertainties are modelled as interval fields . An interval finite element method (IFEM) incorporating interval fields is proposed. Uncertainty propagation analysis is performed by adopting a response surface approach. The proposed IFEM is integrated into the commercial finite element software ABAQUS. Abstract: Finite element analysis of linear-elastic structures with spatially varying uncertain properties is addressed within the framework of the interval model of uncertainty. Resorting to a recently proposed interval field model, the uncertain properties are expressed as the superposition of deterministic basis functions weighted by particular unitary intervals. An Interval Finite Element Method (IFEM) incorporating the interval field representation of uncertainties is formulated by applying an interval extension in conjunction with the standard energy approach. Uncertainty propagation analysis is performed by adopting a response surface approach which provides approximate explicit expressions of response bounds requiring only a few deterministic analyses. Then, the whole procedure is implemented in ABAQUS' environment by coding User Subroutines and Python scripts. 2D plane stress and bending problems involving uncertain Young's modulus of the material are analyzed. The accuracy of the proposed IFEM as well as response variability under spatially dependent uncertainty are investigated.