Response and eigenvalue analysis of stochastic finite element systems withmultiple correlated material and geometric properties

The variability of the random response displacements and eigenvalues of str uctures with multiple uncertain material and geometric properties are studi ed in this paper using variability response functions. The material and geo metric properties are assumed to be described by cross-correlated stochasti c fields. Specifically, two types of problems are considered: the response displacement variability of plane stress/plane strain structures with stoch astic elastic modulus, Poisson's ratio, and thickness, and the eigenvalue v ariability of beam and plate structures with stochastic elastic modulus and mass density. The variance of the displacement/eigenvalue is expressed as the sum of integrals that involve the auto-spectral density functions chara cterizing the structural properties, the cross-spectral density functions b etween the structural properties, and the deterministic variability respons e functions. This formulation yields separate terms for the contributions t o the response displacement/eigenvalue variability from the auto-correlatio n of each of the material/geometric properties, and from the crosscorrelati on between these properties. The variability response functions are used to compute engineering-wise very important spectral-distribution-free realiza ble upper bounds of the displacement/eigenvalue variability. Using this for mulation, it is also possible to compute the displacement/eigenvalue variab ility for prescribed auto- and cross-spectral density functions. (C) 2000 E lsevier Science Ltd. All rights reserved.