Abstract
Abstract Spatially uncertain parameters are traditionally represented by random field models . However, the large amount of information required for construction of precise probability distribution is often difficult to obtain for many practical engineering problems. In this paper, an interval field model is proposed to represent spatial uncertainties with insufficient information, in which the variation of the parameter at any location is quantified by an interval with upper and lower bounds. The spatial dependency is measured by a covariance function or a correlation coefficient function, defined for the interval variables at different locations. An interval Karhunen–Loeve expansion is formulated for the proposed interval field model, in which the continuous spatial uncertainty is expressed through a series of deterministic functions with uncorrelated interval coefficients. Furthermore, by incorporating the interval field model into the finite element method , interval finite element analysis with spatially uncertain parameters is carried out. Perturbation-based interval finite element methods are developed to evaluate the upper and lower bounds of structural responses such as displacement and stress. A Monte Carlo simulation method is also presented to provide a reference solution for the structural analysis with interval fields. Finally, two numerical examples are investigated to demonstrate the effectiveness of the interval field model and the interval finite element methods.
Highlights
Interval Field Model and Interval Finite Element Analysis
These include material properties of the heterogeneous media such as concrete or porous rock, external loads such as wind or snow loads applied on structures, etc. This type of uncertain parameters is traditionally quantified by the random field model, while the large amount of information required in construction of the precise probability distribution functions is often difficult to obtain for many practical engineering problems
The authors propose an interval field model to represent the spatial uncertainties with insufficient information, in which the variation of the parameter at any location is quantified only by an interval with the upper and lower bounds
Summary
Interval Field Model and Interval Finite Element Analysis State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha, China. Abstract: Uncertain parameters with inherent spatial variability are commonly encountered in engineering.
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