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Summary This paper presents the study on non‐deterministic problems of structures with a mixture of random field and interval material properties under uncertain‐but‐bounded forces. Probabilistic framework is extended to handle the mixed uncertainties from structural parameters and loads by incorporating interval algorithms into spectral stochastic finite element method. Random interval formulations are developed based on K–L expansion and polynomial chaos accommodating the random field Young's modulus, interval Poisson's ratios and bounded applied forces. Numerical characteristics including mean value and standard deviation of the interval random structural responses are consequently obtained as intervals rather than deterministic values. The randomised low‐discrepancy sequences initialized particles and high‐order nonlinear inertia weight with multi‐dimensional parameters are employed to determine the change ranges of statistical moments of the random interval structural responses. The bounded probability density and cumulative distribution of the interval random response are then visualised. The feasibility, efficiency and usefulness of the proposed interval spectral stochastic finite element method are illustrated by three numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

Summary The research work extends the scaled boundary finite element method to non‐deterministic framework defined on random domain wherein random behaviour is exhibited in the presence of the random‐field uncertainties. The aim is to blend the scaled boundary finite element method into the Galerkin spectral stochastic methods, which leads to a proficient procedure for handling the stress singularity problems and crack analysis. The Young's modulus of structures is considered to have random‐field uncertainty resulting in the stochastic behaviour of responses. Mathematical expressions and the solution procedure are derived to evaluate the statistical characteristics of responses (displacement, strain, and stress) and stress intensity factors of cracked structures. The feasibility and effectiveness of the presented method are demonstrated by particularly chosen numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.